1. As bad as the fetch quests were in ME3 they were basically a replacement for planet scanning, a way to break up the combat that made sense in the context of the Reaper War. In Inquisition its worse since it's way more involved and makes no sense. I'm the Inquisitor find your own goddamn goat or lost ring.
2. BSG is a TV series, it starts off as a two hour mini-series which is basically the pilot and then you got 4 Seasons of greatness to watch. The very first episode past the pilot, "33," is one of the best pieces of television ever produced and it's not even my favorite episode. Also, fuck all the haters who dislike the ending it's great.
3. Don't know much about Stargate but there isn't too much Star Wars in Mass Effect since SW is more science fantasy. There are some visual cues and plot similarities. For example, ME2 is basically The Empire Strikes Back and I'd bet my ass off that the last shot in ME2 is a homage to the last shot in Empire Strikes Back. And, I guess you could also say that the Spectres are basically more "realistic" Jedi's, but that's about it.
4. Man, I have to say again you are in for some serious sci-fi greatness. I'd say start off with BSG since there's only 4 seasons, afterwards you can watch either Babylon 5 or if you've never seen Star Trek watch that starting with The Next Generation. And then of course watch ST: Deep Space 9 at which point you'll understand where BSG got a lot of it's ideas.
Heh, I actually don't think I had seen Blade Runner the first time I played ME2 but afterwards when replaying I was like HOLY SHIT, Omega is a blatant homage to Blade Runner as is the lighting used on Illium. The references on Ilium become even more apparent during Thane's mission as you drive the hover car to reach the building and then the final shot of Thane looking out at the sunset through Nassana Dantius' window. Pure Blade Runner.