Need help reinstalling Yosemite/Question about external hard drive
I have an early MacBook Pro and I have to reinstall Yosemite because I've been getting nothing but spinning beach balls, slow loading, lag in type showing up, and wi-fi issues. I took the laptop to the Genius Bar at the Apple store last week and they ran diagnostics on everything and all was perfectly OK. No hardware issues, no memory issue and he said my laptop was very clean. He saw the spinning beach ball many times while he was working on my laptop and suggested that I turn off File Vault as that could be causing the slowdown. He said if that didn't work (it didn't) to buy an external hard drive (which I received today) and to back up everything through Time Machine then reinstall Yosemite. I specifically bought an external HD that says "for Mac" and as soon as I connected it Time Machine opened and did the backup.
Now these are my questions. Are all my photos on iPhoto, and my Word for Mac documents backed up so that when I reinstall Yosemite, everything is going to be right where I left it? Will I lose Word for Mac and have to reinstall it? Isn't Word for Mac a one time use/install and will I have trouble and have to call Microsoft to input my authentication key in again and will they let me? I know silly questions but I'm really worried about losing stuff.
Also step-by-step detailed instruction on how to reinstall Yosemite would really be appreciated. Thank you!
MacBook Pro, Mac OS X (10.6.8)