Multiple Text Box Issues for a Beginner

[bplus]

The first issue is that I can't figure out how to take a screenshot of one particular area of the screen

This is combo of maybe _Newimage, for sure _Putimage and _SaveImage.

_putimage gets a section of screen and can put it into a _newimage work area and _saveimage can convert that image to file for storage and retrieval anytime anywhere.
You might just be needing to learn to use _PutImage: https://qb64phoenix.com/forum/showthread.php?tid=1119

"Text boxes"
I know "text boxes" as controls in GUI that users use to fill with strings for processing info in the app.

This is not describing them:

The purpose of this is for the second issue, and for all I know isn't needed at all. I made code to animate the opening of a text box by splitting it into thirds. It appears from top to bottom over a certain period of frames. But the problem is that the only way I've been able to make those images disappear is by making them all disappear at the same time. However I simply want the animation to reverse itself so the box appears to be closing.

Could you be talking about View Print or Window commands used for controling areas of screen usually for text?

Pete says post code and usually that is great advice for newbies but trying to describe things with right words won't be helped much by code.

It seems like you are going for some visual effect with text? You can use _NewImage and _PutImage to create all sorts of effects with text like swirl it around with RotoZoom!