My grandparents live in a house that's about 100 years old. I have no
idea how old the wiring is in that house but I'm fairly certain it
hasn't been changed in 20 to 30 years.

They have two 10-20 y/o refrigerators and two 30+ year old freezers.
Downstairs they have three window A/C units running and upstairs they
have two window A/C units running. Plus things like tvs, a computer,
and lights. I'd really hate to see their electric bill.

The other day I was there and something happened that concerns me. The
A/C was on in a bedroom and we were vacuuming in the room. Some time
after that (maybe 5-10 min) I noticed that the A/C had stopped working.
Grandpa went to check the breaker and everything was ok. So I plugged
the A/C into the top outlet and it worked. I then plugged it back into
the bottom outlet where it had been and it wouldn't work.

What would cause the bottom outlet to stop working?

It has me concerned because they do the dumbest and unsafe things
sometimes. I saw them plug a three prong A/C into an adapter that
converts it to two prongs, then they plugged it into an extension cord,
then into the wall. So basically, they had the A/C running of an
extension cord. I think (not sure) that one of the refrigerators may be
plugged in that way. In the next few weeks they will be getting a third
refrigerator and I know that one will be plugged into an extension
cord. I was always taught that things like that are potentially
dangerous.