Sure re the BER tomatoes. I'd get rid of the buggy ones or you will be growing a whole colony of the bugs in your compost.
All the tender, leafy parts of the tomato plant can be composted IF they are not diseased. If they have blight or septoria or anything, I wouldn't put in the compost pile, just get rid of them. The big heavy tough vine at the base of the plant won't break down very well, unless you chop it a bit.