Hello - from an Axe program, how would I be able to pick an arbitrary picture variable (which is editable by the average user via either the pen command or through manipulating the graphscreen), then copy the contents of the picture to the buffer (or back-buffer, or other such place)?  Also, how would I be able to do the reverse (i.e. to copy the contents of an arbitrary buffer to a picture variable)?

I would also like to know the method for importing a picture variable once at compilation (for elaborate title screens and such).

Also, what is the most commonly used and accepted acronym or abbreviation for 'picture variable'?

Yeah Pic, picvar, or something to that effect.
The syntax to include the data of a picture into a compiled file is this:
[Pic1]->Pic0It inserts the data from TI-OS var Pic1 and makes it accessible through the Pic0 static pointer.
As for reading an arbitrary pic, do you mean in the sense of "a certain picvar I choose at compile time" or "a picvar chosen at runtime, perhaps by user input"?
The first is easy, and can be done like this:
If GetCalc("Pic1")->X
Copy(X,L6,756
EndThis code, if Pic1 exists, copies it to the main buffer.
Dealing with a variable one is a bit harder, and I forget the specifics, but it involves overwriting a byte in the name to change it.
Same situation for writing. Here is code that copies from the buffer to Pic1.
If GetCalc("Pic1",768)->X
Copy(L6,X,768
EndFor both reading and writing an arbitrary one in the second sense, you need the overwriting, but, after you change the name, the general process is the same.
Note what 756 and 768 mean. A picture of size 768 includes the bottom (63^rd) row, but size 756 does not.

Wait, if the size of the screen is 768 bytes, shouldn't picvars invariably also have a set number of bytes?

No
You can create a 2000-byte picvar. The OS won't complain, even if you use RecallPic with it.
756 and 768 are the two most common sizes because the OS uses 756 (63 rows) and 768 is the full screen (64 rows)
Edit: ninja'd. maybe.