Choosing one of these icons, described from left to right, tells Painter 7 to paint or apply some Effects menu options both inside and outside the selection, only outside the selection, or only inside the selection. To read more, see the Painter 7 User Guide, Chapter 12 Using Selections and User Masks, the section named:

"Working with Selections".

The Image Size Pop-up window displays the image's Width and Height in pixels, and
its Resolution (or ppi). It also shows how your image fits on the currently selected printer paper size and orientation. To read more, see the Painter 7 User Guide,
Chapter 3 Basics, the sub-section named:

"Image Size Information".

For lack of a better name, if there is an official one, I call this icon the "Locator" Popup. 
It allows you to quickly view the entire image while still zoomed in to work on detail. The red rectangle shows what area of the image is currently displayed in the image window. 
If you click and drag the red rectangle to another location, that location will then be displayed in the image window, still at the current Zoom percent. 

This is a very convenient feature as it both lets you see the effect of your work on the overall image, and lets you move quickly to another location to continue working, without the bother of having to zoom out, move the image with the Grabber tool, zoom in again, then use the Grabber tool to reposition the image.

Among other ways of controlling Zoom percent, you can click and drag the Zoom Scale slider or type a specific Zoom percent number in the Numerical Setting Field (that's what
I call it). In the image above, the Numerical Setting Field has been clicked and it's ready to have a new number typed in.