[SalesForce] Using makes the labels disappear

Well, since you are already using labels as fields in the controller, why not simple render their value with a standard binding?

E.g. controller:

public class MyController
{
    public String mylabel1 {get; set;}
    public String mylabel2 {get; set;}

    public MyController()
    {
         mylabel1='label one';   
         mylabel2='label two';   
    }
}

VF page:

<apex:page Controller="MyController">
    <span> {!mylabel1} </span>
    <span> {!mylabel2} </span>
</apex:page>

Should you by any chance try to add a binding referencing a field which does not exist in the controller (e.g. mylabel3), you won't be able to save your changes as you will get Save error 'Unknown property'.

Action Regions require a reRender attribute to be effective. The point of an Action Region is to refresh only part of the page, using only the data that is contained in the Action Region. This is commonly used to isolate apex:inputFile fields, which can't be used with reRender at all, and also to avoid validation errors that may occur while trying to update the page while some standard validations exist in the page.

If you have identified a use for an Action Region, you must also be prepared to use reRender, because the two work hand-in-hand. When you do not use a reRender attribute, the entire page state is submitted and validated before attempting to run any controller logic. Using the Action Region will restrict validation to just that section of the page, but also usually prevents updates from occurring outside the action region area.

Traditionally, I've used this to do things like loading a contact's address fields into the page when the contact is changed in a lookup field. Validation rules could prevent this code from running successfully, and so the Action Region serves as a way to isolate part of the page and allow the controller to run normally when it otherwise would produce Visualforce errors.