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What items need to dispose when closing activity?

What elements need to dispose when i'm closing an activity?
I'm using lists,sqlite,recyclerview,listview and so on. If i will call finish inside an activity, doesnt dispose all my activity elements-objects even they are not null?
finish();
finishAffinity();

Certain elements in Android will continue to exist after your Activity has finished, such as BroadcastReceivers.
These elements need to be unregistered when your Activity finishes to avoid things like memory leaks or other weird behavior.
There's no definitive list for this, because it's assumed you will read the documentation of each respective class or API you use and know whether or not it needs to be unregistered/destroyed along with your Activity.

Generally, java's garbage collector will take care of disposing any objects that are not required anymore, however, as #TheWanderer already said, some objects need to be deregistered. Again, please read the docs of the classes you're using as they will indicate if they need some special treatment.
(Hint: Place the cursor in the class name that you want the documentation for and press Ctrl+Q in Android studio to view the documentation)

Android: Creating a new instance of a new activity

I'm confused regarding with some basic android development concepts, my question is not pointing at a particular code, thats why I dont include any.
Let's say that I have an activity inside of which I have a container in which I load a couple fragments (they are multiple instances of the same fragment), now the activity is populated, and inside one fragment I press a button that opens a new activity, it doesn't matter what may happen in that activity, the thing is that when I press a button it should take me back to the previos activity, I know that pressing the back button or using .finish(); will take me back to my already-populated activity, but I want to know, if that is the correct thing to do, or should I finish the activity as soon as i leave to the next one and when I want to go back create a new instance and repopulate it, if so, where should i store the variables?
Let's say that the fragments that I mentioned are "alarms" for an alarm application, and when I create it I call AlarmFragment newAlarm = new AlarmFragment(); and then I add that alarm to an arrayList in my alarms activity (java class) getListOfAlarms().add(getAlarmsAmount(), frag); which remains on the activity that has the fragment container, the question is, are these variables created in the right place? Because I am leaving them inside the activity itself right? What could happen if the activity is destroyed? I've been told that I should create an SQL database for storing those variables. I am not talking about long term saving but variables that I will be using at runtime
Can someone explain me these concepts a little bit? A link to a place where it is explained will be great too.

Your question seems like it has many parts.
In Part 1, this is what I think you are talking about:
1) how you decide to allow the user to get back to the first activity is really up to you. And 2) what you leave in the Back Stack is also up to you and what you want to define for the users' capabilities within your app. For example, if you want them to only be able to use a button that you define inside Activity 2 container, that is fine. However, you are not required to provide a button in Activity 2, and you are certainly allowed to use the Up Action in the App Bar for navigation. If I were you, I would read more about the Tasks and the Back Stack http://developer.android.com/guide/components/tasks-and-back-stack.html
You also mention this idea of having to "finish an Activity" with .finish(). I don't think that is usually necessary, but it is available to you if you want to use it based on what you decide for your app's logic (and what the user should and shouldn't be able to do).
With the Back button, Activity 1 will appear as if just initialized when you get back from Activity 2. Try it out. Also run some Log statements based on the simple diagram I provided and the Lifecycle "callbacks" (put these methods in your Activities and throw a Log statement in each to get a better sense of where you are in the Lifecycle) http://developer.android.com/guide/components/activities.html#Lifecycle
As for Part 2 of your question, I would try/set-up some of the above first, then start to experiment with a single variable to see what happens to it between Activities. There are a lot of "what ifs" to your question. You don't necessarily have to create a DB to store your variables, but that could certainly be an option. Take a look at the Developer Guide for most of the Data Storage options: http://developer.android.com/guide/topics/data/data-storage.html
If you are concerned about losing data when the Activity is destroyed, I might consider creating a database. Read the following for more info on recreating an Activity when you have gone elsewhere and are returning: http://developer.android.com/training/basics/activity-lifecycle/recreating.html In particular Saving Your Activity State: http://developer.android.com/training/basics/activity-lifecycle/recreating.html#SaveState
There's also an SO post on this: Saving Android Activity state using Save Instance State

Best practice to persist android "home"/"main" activity?

I have an android app with one "home" or "main" activity that relies on fragments to accomplish several tasks. This data relies on information retrieved from a server (mine, and presumably a substantial amount by google maps).
I would like to structure my code such that several other activities (ie. preferences) can temporarily take focus before returning to the main activity.
Currently android destroys and recreates the main activity, which means bandwidth is wasted every time.
There are several notable intent flags which 'solve' this problem (Intent.FLAG_ACTIVITY_REORDER_TO_FRONT and Intent.FLAG_ACTIVITY_CLEAR_TOP), however they only appear to be useful when transitioning back to the main activity, which means I have to #override the system behaviour for both onKeyDown() and onBackPressed(). I would really prefer not to do this in case it causes other issues or eventually becomes deprecated.
Is this safe? Or is the better solution to force my application to create a serialization (savedInstanceState) of the main activity and all fragments anytime another activity temporarily takes the foreground?

Using saved instance state is the proper approach here. That will let you persist the information retrieved from the server when the activity gets re-created.
You only need to implement code to save / restore the instance state in the fragment or activity that holds the data. If you want to share that data across all your fragments, you can place it in the activity and add code to save the instance state of the activity. Then you can access the data that's stored in the activity from your fragments with ((MainActivity)getActivity()).getData().
For code to save and restore instance state, take a look at:
http://developer.android.com/training/basics/activity-lifecycle/recreating.html#SaveState
http://developer.android.com/training/basics/activity-lifecycle/recreating.html#RestoreState
If the data you need to persist is really large, you can use a retained fragment instead, as explained here:
http://developer.android.com/guide/topics/resources/runtime-changes.html#RetainingAnObject
Another trick for large data objects is to use a singleton class to store the data while the orientation change takes place.

Android - How to tell what Activities are currently open?

I'm falling into a bit of a dilemma. As I learn more and more about Android and Java, the more confused I am about the state of the building blocks of Android apps. (i.e. Activity, Service, Broadcast Recievers, Content Providers)
Since all of those building blocks are just Java classes, it's tough for me to wrap my head around them because there can be multiple instances of them. As of late the biggest challenge is with tracking which instance of the Activity is actually being created, started, resumed, etc;. I started playing around with Intent flags, and that just threw another wrench (or ten) into the equation.
Being able to tell their state would be indispensable and even better would be to see the current task stack/process id that the activity is associated with. At this point I'm just guessing whether or not FLAG_ACTIVITY_NEW_TASK, FLAG_ACTIVITY_CLEAR_TOP and FLAG_ACTIVITY_SINGLE_TOP are working properly.
Surely there is a solution. Is there any debugging tool that I can use to get an inside view of my app/process to see which components (specifically Activities) are in existence?
Some notes/thoughts I've had:
Should I create a unique static auto-increment int for each class to try and track it myself?
Is this what I want Get current visible activity to user?
Does this application manually keep track or is it really peaking inside of the process? https://play.google.com/store/apps/details?id=com.novoda.demos.activitylaunchmode
There has to be a debugging tool for this... -__-

Not sure if this will solve your understanding of the topic completely, but these guys did a nice app to try and visually see the main launch modes available for Activities > https://play.google.com/store/apps/details?id=com.novoda.demos.activitylaunchmode&hl=en_GB
Hope this helps in some way to explain things! :-)

android : Can we implement a single dialog showing error, if multiple activities in a flow crashes?

When a single activity crashes, all the activities in flow crashes.
As all activities crash, each generates its own error dialog, so can we have a single dialog for all crashes?
Try catch is already implemented.

You use a singleton static final object to handle all your diablog boxes across all your activities. One such singleton object is the application object, see http://developer.android.com/reference/android/app/Application.html, but you don't have to use that one if you don't want to.
Also, you have to make sure that try/catch is implemented absolutely everywhere, wherever the android operating system makes calls into your app code. I'll find that I've got try/catch in most places in my code, but somehow when I'm trying to develop quickly I accidentally miss a few places and of course they're the ones that end up causing me a problem!