Will a week long break from invisalign affect my results? (Photo)

No problem with leaving them out a wee, until your swelling go down. After a week has pass, you can placed the aligner #8 back in, if that is the aligner that you are on. If #8 aligner does not fit, you can go back to aligner #7, and it should fit.

You should check with your doctor after the week end to make sure the fit is still good, but it shouldn’t drastically effect your treatment. It is important that the gum has a chance to heal. You might need to wear the next tray slightly longer to make sure teeth have enough time to move.

It's okay to take a break from the tray for a few days.  Just note that you will have to wear that tray longer.  It would also be good to cut off the back molar so it doesn't interfere with the tissue and continue to wear your current trays.

It will make a difference.  Take your last set of aligners (you are saving them of course) and use nail clippers to trim off the back molars and wear them at night until  you can get back to the current ones.  If you did not save the last ones, use do the same to the current ones and be prepared to wear the following set a little longer