I have a few fallout 1 questions. Can I use my save from the old CD versions? Also, the old CD version goes black and I need to paint the screen every 10 min or so. Does this version do that or has it been fixed?

Well, since noone has black screen problem here, I guess it IS fixed :D
I guess saves should be compatible, but... Well, you can always try :D

I get that issue with the black screen on mine as well, there is a fix for it however, someone in these forums, I forget where. I think people were saying the resolution patch might be able to fix this.
http://www.nma-fallout.com/forum/dload.php?action=file&file_id=1169
but I'm using it and it hasn't fixed the issue for me.

I vaguely remember fixing that glitch in the distant past (~4 years ago) by toggling the Mouse Pointer mode (hardware/software). Try flipping that switch and see if it helps.
If not that, look into running the game in DOS compatibility mode. You can find this option by right-clicking on the main executable (fallout.exe?), choosing Properties, and going to the tab marked Compatibility.

If the save game is patched to the latest official version, it should not be any problem.
I've had that in my GoG.com version.
Closing any applications that had a "pop-up" element in them fixed it though. (For me it was Winamp)