Make sure your mother board has the appropriate slot for the gpu you are installing.
Make sure your case can fit it too. Video cards are monsters now. Also, you need to make sure your power supply has an additional 6-pin connector because video cards need an extra power source.

1. Is it true that when i purchase a copy of Windows 7 Ultimate 64bit, that i can put the CD in my PC while it's running Vista and go through prompts and install it just as if i was installing a PC game?
You can upgrade any version of
Vista 64-bit to any Windows 7 Ultimate 64-bit.
To sum it up. Home Premium can only upgrade to Home Premium or Ultimate. Home Basic can only upgrade to Home Basic or Ultimate.
2. When i do this will i have to back up files on my computer such as saved Word Proccesor Documents?
You should back up your files before doing an upgrade.
3. I purchased Microsoft Word for my PC three years ago and i lost the install CD while moving from Indiana to Georgia. Will i have to purchase/install Word all over again when i upgrade my OS?
Yes, it will work. Windows 7 is basically Vista 2.0.
4. When my Uncle was still alive, he once showed me a place online after i paid like 300bucks for Vista that i could have actually purchased it for like 100 bucks instead. Does anybody know if i can do this for Win 7 Ultimate 64bit?
You can buy a working Win 7 ultimate key for $30 online. You will have to burn a copy of Windows Ultimate yourself.
5. When i purchase my new video card, how exactly do i go about installing it? My current theory is this(please correct me if i'm wrong):
a. Turn of my PC, unplug everything from the tower
b. Remove current video card from motherboard
c. Put in new video card into Motherboard
d. Reboot the PC
Note: if this is how you correctly do it, what will happen when i reboot my PC?
That is the correct option. If it is done right then your monitor will turn on.

6. What should i do first? Upgrade my OS, then upgrade my video card, or vise versa?
Easier to upgrade OS then video card IMHO.