Hm, I'm not as knowledgeable as all that... strictly a beginner in this direction.
I think, if your TP7.0 is similar to TP6.0, that the DOS-shell is a temporary escape into the DOS environment in which the turbo editor/compiler is operating, in which case you're probably doing the right thing. But to be sure it might be worth compiling your program to disk (i.e. make the exe file), then go to a dos window (or dos shell from the TP editor), and run the tsr, followed by the program as a compiled exe file, because then you are absolutely certain that the tsr is resident at the time the program is run.
Batch files have the file extension .bat, and are simply text files containing instructions that you could type at the dos prompt. You can write then in notepad or your pascal editor. If you want to run a tsr followed by a normal program, you just need a text file with two lines, the first containing the name of the tsr, the second the name of the program, and the whole file called something like name.bat. Then, when you type 'name' at the dos prompt, it's as though you'd typed everything in the batch file.
Yes, with 640*480 you should be fine. If you ever get interested in self-made mice, you'd need to find out about interrupt 033h, which deals with all the communication with the mouse. It also has a call where you can specify a procedure that will be called every time some mouse event occurs (and you specify a filter on what events should trigger it), for instance every time the mouse moves. You can then write your own procedure that draws a mouse pointer and use this mechanism to get it called every time the mouse moves. The process isn't trivial because the mouse might move while, for instance, your program has called DOS to do something with a file, or collect a key press from the keyboard. In this case the data segment will be that of DOS, not your program, so all your variables will be wrong... So writing the mouse drawing procedure is a bit interesting and requires some fiddling around in assembler, a process best avoided if possible.
Good luck