Betta’s can go a lengthy time without food. 11 days is stretching it, but it should be OK. I’d recommend feeding pellets leading up to the day you leave and before heading out the door a final meal of bloodworms.
As for water changes, the 5g should be okay to leave undone for 11 days. Try and do a 100% on the day you leave or just before it. As for the 2g it is going to be a bit of a hazard – do you have a sterile container capable of holding 5g+? (tuppaware, plastic container etc) If so, you could turn this into a makeshift larger tank – this would mean it could go the 11 days with a much higher success rate than the 2g.
As Snap said, there are auto-feeders for fish. However you will find the portion control is lacking for Betta tummys, Betta pellets and flakes could be put in but the release mechanism would allow too much out, overfeeding. You could test this yourself to see if you can adjust an amount close to their regular number – trying towards 8 max per day, if it feeds a little more that could be acceptable, just ensure it skips a day with no food to allow the digestion.