I'd recommend you get yourself a meter and do some continuity testing before you start randomly replacing parts. It's a lot cheaper.
According to the Haynes manual (which I highly recommend you get) that's the Starter circuit cut-off relay you are pointing to in your picture. The Haynes manual...
Glad to hear it wasn't too hard for you to get those bolts out. I think they were installed with red Loctite on my 2013. I tried the rubber mallet method, a big breaker bar, and they won't budge without heat.
The install instructions that come from SW-Motech are pretty clear.
It's an easy install except the two bolts you have to remove to install the spring bracket are a real bitch to get off - they require a lot of heat to get them to break loose.
I thought about it - the front brakes on my 2005 R6 really spoiled me. I found that the 03-04 R6 or 06-09 R6S used the same size rotors and the calipers should bolt right on the FZ6R. To do it right, you'd also need the R6 master cylinder.
I decided against doing it when I figured out the cost...
What needs to be done really depends on how the previous owner stored it - because he obviously didn't ride it very much.
If he kept it on a Battery Tender, the battery may be fine, otherwise it should probably be replaced.
Personally, I never trust anyone regarding the fluids and I change...