Unfortunately old programs are the only ones that are available for the IIe. No one has written a commercial program for the II line in about 10 or 15 years. There are one or two people who have written a new game or two, but those are few and far between and are simply done by users like us. What type of things do you want to do with the IIe? If you can give us an idea we can possibly recommend programs.
As to your your problem with Battle Chess what monitor do you have the computer hooked up to? That might be the source of your trouble with the blurry screen. As to Chessmaster I'm not sure why it's giving you trouble. I'll try copying it to my GS and see if I can get it to work.
One possibilty you could explore is trying to learn to program the IIe yourself. That way you can come up with a program to do, hopefully, exactly want you want to on the computer. Applesoft is an easy to use language that is built into the IIe. Other prgramming languages can be downloaded from Asimov and other sites on the web. So your options are wide open.
Magnus
Apple II Forever