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What is the equivalent of JSTL <c:forTokens> in JSF or PrimeFaces?

Assume we have the following JSP code:
<c:forTokens items="${someBean.aStringOfIntNumbersSeparatedBySemicolons}"
delims=";"
var="item"
varStatus="stat">
${item}
<c:if test="${!stat.last}">;</c:if>
<c:if test="${stat.count %5 == 0}">
<br/>
</c:if>
</c:forTokens>
Of which the output is rendered in rows with 5 columns each, like so:
How can I possibly do this with the JSF or Primefaces tags?

There is no direct equivalent, you should transform your token into a list in the managed bean and consume the list in the framework components.
List<String> tokens = Arrays.asList("car1,car2,car3,car4".split(","));
For such simple scenario you might not need the primefaces components. When you go for a Object Oriented model, you can take advantage of PF components to iterate through the list and present its fields using data binding. For instance:
DataList - For each Car type in the cars1 list, a line will be added in the list.
<p:dataList value="#{dataListView.cars1}" var="car" type="ordered">
<f:facet name="header">
Basic
</f:facet>
#{car.brand}, #{car.year}
</p:dataList>
DataTable - For each car in cars list, a row is added to the table component.
<p:dataTable var="car" value="#{dtBasicView.cars}">
<p:column headerText="Id">
<h:outputText value="#{car.id}" />
</p:column>
<p:column headerText="Year">
<h:outputText value="#{car.year}" />
</p:column>
<p:column headerText="Brand">
<h:outputText value="#{car.brand}" />
</p:column>
<p:column headerText="Color">
<h:outputText value="#{car.color}" />
</p:column>
</p:dataTable>
Using such component framework you might speed your development focusing on the business logic instead of UI design.

The only working solution I've found
For now, the only working solution I've found lies partly in the JSF and partly in the back-end code:
Edit the back-end code so that it adds a <br/> after every fifth element of that String field aStringOfIntNumbersSeparatedBySemicolons.
Add escape="false" to the <h:outputText> tag that holds the data on the front end. (The default value is escape="true", which renders <br/> as <br/>)

primefaces filterby function gives no results

I am trying to filter a datatable by adding the following code:
<p:dataTable value="#{hoofdschermBean.onderzoekers}" widgetVar="onderzoekerTable" var="onderzoekeritem" rendered="#{not empty hoofdschermBean.onderzoekers}" rowStyleClass="tablerow" draggableColumns="true">
<f:facet name="header">
<p:outputPanel>
<h:outputText value="Zoeken:" />
<p:inputText id="globalFilter" onkeyup="PF('onderzoekerTable').filter()" style="width:150px" placeholder="Enter keyword"/>
</p:outputPanel>
</f:facet>
However it does not filter when I fill something in this textbox, it says no records found.
If I add filterBy on a column, only than this textbox can filter on the column variable. What am I doing wrong here?
(P.S. I do not want to have filter functions on every separate column, that is why I wanted this facet only!)
#Edit 14:32 27-11-2014
I have also tried to use
filteredValue="#{hoofdschermBean.gefilterdeOnderzoekers}"
and to use ViewScoped and SessionScoped.

Do you have a List<> field in your managedBean so the filtered values can be saved somewhere? Also, you'd need to reference this value with a filteredValue="#{hoofdschermBean.filtered...}"attribute in your dataTable-Tag.
(Like in the PrimeFaces ShowCase, where they have a List<Car> filteredCars; in their managedBean)
Also, it might be helpful to check the scope of your ManagedBean

Server side listener for rich:dataScroller (RF 4.1)

I'm using an extendedDataTable because I need multiselect. The table can get pretty large, so I'm using a dataScroller for paging.
What I want to achieve is, that the selection is cleared when switching to another page. The selection is stored in the backing bean and I have a method clearTableSelection to clear the selection.
Now my question is, how is it possible to call the method clearTableSelection when switching pages.

I found a simple solution:
...
<rich:extendedDataTable>
...
<f:facet name="footer">
<rich:dataScroller
onbegin="document.getElementById('form:hiddenButton').click()" />
</f:facet>
</rich:extendedDataTable>
<a4j:commandButton
id="hiddenButton" action="#{backingBean.clearTableSelection}"
value="HiddenButton" execute="#this" style="display: none;" />
...

Rules for ids to update components

I'm new to JSF2 and Primefaces and realized an issue to update components.
Lets' assume I have the following piece of code, I can directly update="counter"
<h:form id="f1">
<h:outputText id="counter" value="#{clientBean.counter}" />
<h:graphicImage url="/images/circle-ok.png">
<p:ajax event="click" update="counter" process="#this"
listener="#{clientBean.tag}"/>
</h:graphicImage>
</h:form>
In another h:form I have to use update="f1:counter". Only a update="counter" does not work here.
<h:form id="f2">
<p:dataTable var="var" value="#{clientBean.vf}">
<p:column>
<f:facet name="header">Tag</f:facet>
<h:graphicImage url="/images/circle-ok.png">
<p:ajax event="click" update="f1:counter" process="#this"
listener="#{clientBean.tag}" />
</h:graphicImage>
</p:column>
</p:dataTable>
</h:form>
I haven't faced this with JSF1.2 (and RichFaces), what are the rules to address the ids correctly?

In your first example JSF could lookup up the counter element in the same scope as ajax listener. Form implements NamingContainer which means it prefixes client ids (used in html) with its own id and creates a distinct name space for ids. Have a look at the page source under browser - there will be f1:counter id assigned to your counter. In your second example there is no counter element in the scope (inside form f2) so the lookup fails.
You can disable this form behaviour with prependId="false". This is useful if you are sure there won't be elements with identical ids across all forms.
Icefaces works differently - it automatically calculates the html delta and sends it to the browser as partial update. In most cases this is more convenient for the programmer but comes with considerable performance cost. I believe JSF2 adopted icefaces partial updates concept but requires ids to be passed explicitely.

Primefaces DataTable - Filtering [column not filtering]

I am trying this example 'DataTable - Filtering'. Everything works except for the Search all fields: textbox that filters. when i enter characters to it it doesn't filter as in the example.
There is no errors or exceptions thrown. I don't undestand what onkeyup="carsTable.filter()" does in the code. can someone explain this ? and any idea why it fails to filter
<f:facet name="header">
<p:outputPanel>
<h:outputText value="Search all fields:" />
<p:inputText id="globalFilter" onkeyup="carsTable.filter()" style="width:150px" />
</p:outputPanel>
</f:facet>

carsTable is the name of the datatable. Somehow its missing from the example, but the p:dataTable should have an attribute widgetVar="carsTable". onkeyup is the event that is firedafter you released a key. It tells the carsTable to filter after you entered a new character.
So add the widgetVar="carsTable" attribute to p:dataTable and you are good to go.
If you have a look at the PrimeFaces userguide, you will find the correct example.