We Keep Coding

Can a Gradle project rebuild its dependencies, track their source changes etc.?

I am used to specifying project dependencies in ant/Netbeans, where a project recompiles if its dependency (another, otherwise separate project) changes, "clean and build" cleans and rebuilds dependencies etc. There is also source code navigation, where Netbeans switches seamlessly between projects.
Now I want to learn Gradle, but I was told that I should use a repository for accessing dependencies, like Maven Central. Project dependency configuration in Netbeans UI, in case of a Gradle project, is gone. Thus the question: is the aforementioned possibility of a deep integration between a project and its dependencies possible in a Gradle project?

For your project's source, meaning the stuff under the typical src/main/java, Gradle will "cache" this out of the box for most built-in tasks.
In Gradle, this is known as Up-to-date checks (AKA Incremental Build):
Once your source files have been compiled, there should be no need to recompile them unless something has changed that affects the output, such as the modification of a source file or the removal of an output file.
If you have a custom build task defined or a task that requires to be incremental (cached), then you'll need to follow this to make your custom task incremental.
And for the following:
"clean and build" cleans and rebuilds dependencies etc.
Gradle does not "build" dependencies. It will retrieve dependencies from the configured repositories in the project and then cache them.
You can configure the build cache if needed to suite your needs: https://docs.gradle.org/current/userguide/build_cache.html#sec:build_cache_configure

Gradle Plugin dependency

What is the exact dependency I need to develop a Gradle Plugin in Java? Ideally I would like to get it from a well-known repository such as Maven Central or similar.
I have a Maven project with a core functionality and I just added two extra plugins, one for Ant, one for Maven. They are already tested and working; easy! Now, I wanted to add a third module for a Gradle plugin to make this functionality also available from any Gradle project.
However, I can't find the exact dependencies I need to develop a Gradle plugin.
The Gradle docs (such as https://docs.gradle.org/current/userguide/java_gradle_plugin.html) are not very well written to say the least. They mention:
the gradleAPI() dependency
or the java-gradle-plugin dependency
But they are quite unclear... no group, no version (really?).
If anyone can enlighten me to where I can get these dependencies from, I would be very thankful.

Gradle's public and internal APIs, aka gradleApi(), are bundled with the Gradle distribution and not independently published and therefore not easily consumable by Maven builds. There's the pending epic #1156 (Ensure plugin cross-version compatibility by allowing a user to depend on gradlePublicApi()) that might help here.
Since Gradle plugins are best to be built with Gradle, a pragmatic solution is to invoke the Gradle build from Maven and attach the produced artifact to the Maven build. Andres Almiray (aalmiray) once described this in the blog post Running Gradle Inside Maven (Web Archive Link). He describes the following high level steps:
Create a new Maven module (e.g. gradle-plugin) and add attach it to the parent POM
In the POM of gradle-plugin add a dependency to your core module. Use the maven-dependency-plugin to store dependencies to the Maven build folder, e.g. target/dependencies.
Create the build.gradle, add a Maven repository that points to target/dependencies (step 2) and let it depend on the core module as well as gradleApi(). Implement the Gradle plugin.
Use the exec-maven-plugin to invoke the Gradle build.
Use the maven-resources-plugin to copy the Gradle built plugin jars to the standard Maven build folder.
Use the build-helper-maven-plugin to attach the copied jars to the Maven build.
Sample project to be found here (gradle-in-maven).

https://docs.gradle.org/current/userguide/custom_plugins.html#sec:custom_plugins_standalone_project
In here it is mentioned that it is gradleApi() and I know that this works (from experience). The localGroovy() on that page is only needed if your plugin code uses groovy (does not apply if you only use groovy in the build.gradle of your plugin).
java-gradle-plugin is a library that makes it a bit simpler to make plugins, it is not required though. I personally prefer using gradleApi only.
EDIT:
It appears I've misunderstood the question. Here are the steps to get gradleApi jar:
Create a Gradle project with your desired Gradle version.
Add implementation gradleApi() dependency.
Import/run the project once.
Go to your .gradle folder (located in home folder in Linux-based operating systems).
Open caches folder
Open the version folder you want, e.g. 6.0.1
Open generated-gradle-jars folder.
Copy the jar to wherever you want and use it.
For me the 6.0.1 jar is at ~/.gradle/caches/6.0.1/generated-gradle-jars/gradle-api-6.0.1.jar
Please note that I have not tested this, I know the jar is there but I haven't tried using it.

Installing a framework without maven or gradle

I try to install Javalin framework for creating an API on my Java project. (old java 8 project without maven, gradle, etc). I would like to install the framework with adding the jars to my build path.
But If I add the main jar file then it needs another dependencies jar , then another one another one another one.. etc.
Is there any simple way to add this to my project and all it's dependencies without any build tool like Maven,etc?
I have tried adding it manually , but each jar has many dependencies that it is almost impossible(?)

Well you could create a Maven project and use it to download the dependencies for you.
Maven dependency plugin might be useful. With it you could just call:
mvn dependency:copy-dependencies
and it will download all your dependencies into target/dependency.

I don't think there's a way, I'm afraid.  Dependency management is the exact problem that build tools like Maven and Gradle were created to solve!
The framework supplier could provide a ‘fat’ jar including all the dependencies; but I'm not aware of any that do, as everyone uses Maven or Gradle (or SBT or Ivy or Grape or Leiningen or Buildr).
I think the only real alternative is to do it manually — which, as you've discovered, can be a horrible and lengthy task if the dependency tree is big.  (And would need redoing with every update.)
So I'd suggest biting the bullet and using Maven if you can.

How to bring all dependencies jars with Gradle?

I have simple java (Gradle) project wich depends on several JARs, obtained automatically from Maven repositories.
Now I wish to call my jar with external application (Matlab). Unfortunately, application does not see any dependencies after I call build, jar and similar goals.
Me myself also don't know dependencies, since they are managed automatically with Gradle and may contain nested dependencies, not listed in build.gradle.
Is it possible to collect all required JARs in one place to run them freely?

You can write a custom task to collect your runtime dependencies into a jar
task copyToLib(type: Copy) {
into "$buildDir/libs"
from configurations.runtime
}
You could also look into the application and distribution gradle plugins, that provide similar packaging and distribution functionality

Including .jar files in Github for consistency

I am new to using github and have been trying to figure out this question by looking at other people's repositories, but I cannot figure it out. When people fork/clone repositories in github to their local computers to develop on the project, is it expected that the cloned project is complete (ie. it has all of the files that it needs to run properly). For example, if I were to use a third-party library in the form of a .jar file, should I include that .jar file in the repository so that my code is ready to run when someone clones it, or is it better to just make a note that you are using such-and-such third-party libraries and the user will need to download those libraries elsewhere before they begin work. I am just trying to figure at the best practices for my code commits.
Thanks!

Basically it is as Chris said.
You should use a build system that has a package manager. This way you specify which dependencies you need and it downloads them automatically. Personally I have worked with maven and ant. So, here is my experience:
Apache Maven:
First word about maven, it is not a package manager. It is a build system. It just includes a package manager, because for java folks downloading the dependencies is part of the build process.
Maven comes with a nice set of defaults. This means you just use the archtype plugin to create a project ("mvn archetype:create" on the cli). Think of an archetype as a template for your project. You can choose what ever archetype suits your needs best. In case you use some framework, there is probably an archetype for it. Otherwise the simple-project archetype will be your choice. Afterwards your code goes to src/main/java, your test cases go to src/test/java and "mvn install" will build everything. Dependencies can be added to the pom in maven's dependency format. http://search.maven.org/ is the place to look for dependencies. If you find it there, you can simply copy the xml snippet to your pom.xml (which has been created by maven's archetype system for you).
In my experience, maven is the fastest way to get a project with dependencies and test execution set up. Also I never experienced that a maven build which worked on my machine failed somewhere else (except for computers which had year-old java versions). The charm is that maven's default lifecycle (or build cycle) covers all your needs. Also there are a lot of plugins for almost everything. However, you have a big problem if you want to do something that is not covered by maven's lifecycle. However, I only ever encountered that in mixed-language projects. As soon as you need anything but java, you're screwed.
Apache Ivy:
I've only ever used it together with Apache Ant. However, Ivy is a package manager, ant provides a build system. Ivy is integrated into ant as a plugin. While maven usually works out of the box, Ant requires you to write your build file manually. This allows for greater flexibility than maven, but comes with the prize of yet another file to write and maintain. Basically Ant files are as complicated as any source code, which means you should comment and document them. Otherwise you will not be able to maintain your build process later on.
Ivy itself is as easy as maven's dependency system. You have an xml file which defines your dependencies. As for maven, you can find the appropriate xml snippets on maven central http://search.maven.org/.
As a summary, I recommend Maven in case you have a simple Java Project. Ant is for cases where you need to do something special in your build.