Rerender Visualforce component & reload parent window on close

Part of my page:

<apex:pageBlockSection collapsible="false" title="3. How is marketing budget used?" id="thirdQuestion">
	<apex:outputPanel id="thirdQuestionOne">
		<apex:selectCheckboxes value="{!selectedBudget}" layout="pageDirection">
			<apex:selectOptions value="{!budget}"/>
			<apex:actionsupport event="onclick" action="{!CheckRendered}" rerender="thirdQuestionTwo" status="status"/>
		</apex:selectCheckboxes>
	</apex:outputPanel><br/>
	<apex:actionStatus id="status" startText="Please wait..." stopText=""/>
	<apex:outputPanel id="thirdQuestionTwo" rendered="{!isSubSelectRendered}">
		<apex:selectCheckboxes value="{!selectedPlatforms}" layout="pageDirection">
			<apex:selectOptions value="{!platforms}"/>
		</apex:selectCheckboxes>
	</apex:outputPanel>
</apex:pageBlockSection>

Important code pieces of my controller:

// Data Variables
public list<String> selectedBudget {get; set;}
// Control Variables
public Boolean isSubSelectRendered {get; set;}
public CancellationReportController()
{
	isSubSelectRendered = false;
	selectedBudget = new list<String>();
}
public list<SelectOption> getBudget()
{
	list<SelectOption> options = new list<SelectOption>();
	options.add(new SelectOption('PRINT','Print'));
	options.add(new SelectOption('FAIR','Fairs'));
	options.add(new SelectOption('ONLINE_SHOP','Investment in own online shop'));
	options.add(new SelectOption('WEBSITE','Investment in own website'));
	options.add(new SelectOption('NOTHING','No activities planned'));
	options.add(new SelectOption('OTHER_PRESENCE','Presence on other platforms (please specify)'));
	return options;
}
public void checkRendered()
{
	if ( new set<String>(selectedBudget).contains('OTHER_PRESENCE') )
	{
		isSubSelectRendered = true;
	}
}

When i simply render the second output panel neglecting the controller boolean value, I see that panel on the page and can use it, so it is set up correctly. What I do not know is where I have to put the action support tag or how I can make it do more than simply displaying the status and actually rerender the second output panel.

I have a save button, which calls the save function in the controller and then closes the form window on completed calculations.

<apex:pageBlockButtons>
	<apex:commandButton action="{!save}" value="Save" id="SaveButton" oncomplete="window.top.close();"/>
</apex:pageBlockButtons>

The form was initially called by a salesforce Formula field using the HYPERLINK() function as below: