Well, here's your answers:
(1) Yes, Linux installer Disks are bootable. Infact, there are Linus distros designed to be only booted from the CD.
(2) They cannot run Windows programs, EXEs... however, depending on the Distro (version) of Linux you choose, software is even more available than with Windows. There are programs that handle .ZIP archives no problem, aswell as pretty much every other archive/media/document file format.
There IS a linux program called wine (http://www.winehq.com/ ) that attempts to run Windows EXE programs. It's NOT an emulator or virtual machine, but an actual reprogramming of the Windows interface. It works quite well with simple programs.
(3) See (2). Wine does include some DirectX support, although I've found it very buggy so far.
I always recommend ubuntu Linux (http://www.ubuntu.com/ ) to new users, it's a very easy switchover. Also, here's a great site to learn about Linux... it links to and reviews all the most popular Distros. (http://www.distrowatch.com/ )