It would be helpful if you knew someone who has experience with fixing a flat so they could show you in person.
I've actually "raced" swapping out a tube. It took me less than 2 minutes to pull the old tube out, install the new tube AND pump it up with a floor pump. Add another couple of minutes for a mini pump and another minute to pull the wheel off of the bike and put it back on. That adds up about 5 minutes, but I'm experienced at it. The first one may be a bit longer.
BTW, I can remove and re-install the rear tier without ever touching the chain. It's something that I see people do all of the time, but it's actually easy once you know the technique. Again, seek out someone experienced.