If 10 min is what you can do, do it. As far as other exercise, walking (assuming running would be worse than biking), unloaded squats, lunges, etc. Build some general fitness.

The seat - I'm lucky enough that I've never had major issues, but I definitely feel it in the spring (not a winter biker - too much snow and ice here). You can try a different seat, but that can get expensive quickly. In my experience, it gets better as I ride more, but I've never been in 'agony' from the seat.

The jelly - just means you had a good workout. Consecutive days is hard when you're first starting out, but getting into the routine is important as well. Don't be afraid to take a day off, but try not to do more than one in a row.

Get someone who knows a little about bike maintenance to take a look at your bike - either someone you know who rides and takes care of their own bike, or a shop. That doesn't sound right. Either you didn't have an easy enough gear or there is a mechanical issue.