I actually dig the costumes. Very clean design, logical and evocative of the progress through science that the FF should represent. At this point I have nothing invested in mainstream superhero comics, as I get that kind of material from the library. For instance, I just read volume 1 of Batman & Robin over a year after it was published.
With that said, although this is obviously temporary it's not beyond reason. Team rosters change all the time (look at the revolving door of the X-Men), and it only makes sense that there are close ties between teams. The Thing is, after all, a member of the New Avengers right now. Spider-Man lives in New York City, the Avengers and FF are headquartered in NYC, it's as simple as him getting a call from either team and swinging over to help out.
As well Peter is apparently working at some research facility, Horizon Labs, rather than freelancing as a photographer now, so his association with big brains Reed Richards and Tony Stark is valid. Peter's relationship with Tony leading up to and during the Civil War was criticized, but it made sense that Peter would seek out a father figure and mentor with an intellectual peer. Living in Stark Tower at the time wasn't fitting for the character, but it made sense temporarily.
It doesn't matter, comics ebb and flow, and this isn't much of a shakeup. Over in the Spider-Man monthlies Peter will still live in his own apartment and fight crime solo, and we can assume his Avenger and FF adventures take place off-panel.