-how was your experience with the game?
Fun and generally good/great. One amusing thing happened once when I was watching CSs and my FC team ran into the boss so I got locked out. That was amusing.

-do you think Duty Finder is an overall great system for teamwork?
Teamwork no... trying to herd cats... yes... If you want teamwork get a crew - 3 others will work. The way I see it most of the game revolves around having a group of 4 people. Everything higher is basically get 2 such teams together to do 8 man and so on...

-how can i not come off as a rude person when needing to accomplish achievements?
Mention that you need it and if you can explore fully. As an alternative you can after everyone leaves explore the place for 5-10 minutes. Most mapping will get triggered at the start of the mappable area not at the end so might be enough to just put a foot in the door.