No worries! I love anime!
I take it this was the first time when they met, that you're talking about? The anime did a bad job of that scene, because it did seem completely random. There's a hint however. At the end of the fight, Shachi yells at Kaneki for trying to take him and the Aogiri Tree on. In the manga, the explanation was that Kaneki was aiming to destroy Aogiri, which Shachi had joined.
Nope. There hasn't been any announced plans for a 3rd season for DGM. For now, it stands at 103 episodes and completed. Though they may pick up the story in the future, as they haven't totally scrapped that idea.
myanimelist.com usually has rather reliable information on these kinds of things.
With regards to FMA, it makes logical sense to watch FMAB, because the story gives better closure and it feels more exciting watching it. Also, FMA was a little down on the quality and story compared to Brotherhood, so if you did watch Brotherhood first, be prepared to be disappointed by FMA (if you decide to watch that). Also, the difference in terms of the story between the two is awfully huge. I watched FMA first because brotherhood hadn't come out yet, and I couldn't get into brotherhood after because of the differences.
PS: FMAB follows the manga more closely, but FMA was a little more dramatic (I have to admit).
Any questions, feel free to drop a quote, anytime!