Welcome to LQ!
First off, as you learn your way around here, please pay special attention to the search button. Questions like these are asked on an almost daily basis and you'll find lots and lots of relevant discussion that already exists.
Q1) Linux and Windows will co-exist just fine on a home network. I've got Linux, XP and OSX all living together on my LAN. If you are looking for a relatively easy experience, I'd suggest Ubuntu. It is aimed directly at new Linux users and I've had very good luck setting up friends with it. For a TON of information on distros, I would strongly suggest some quaity time at distrowatch
Q2) If you can dedicate a computer to Linux, that is probably the safest way to do things. The reason I suggest that is that Linux gives you the power to completely bork your system and there is no reason to have to reinstall 2 operating systems unless you have to. If you do want to dual boot, most of the more popular distros will recognize that you have Windows on your computer and help you set up the dual boot.
Q3) You didn't ask this, but I'm going to answer it anyways....A safe way to "test" Linux is using a live CD like Knoppix. Live CD distros work by booting from the CD. Your hard disk is never touched. With one of these you can see if you like Linux without having to go through the trouble of installing in on a box. As long as your rig can boot from a CD, you're good to go. Even if you do install to your hard drive, it is usually a good idea to have a live CD laying around in case of real trouble.