The chasing sounds like mating behaviour. You've probably got a boy and girl in
there.

As for the fish, I would get a much bigger tank for them. Comets and Shubinkins
are
pond fish, but will do well in a bigger tank. I'd suggest a 40 gallon minimum
(you only
have a 15 gallon (approx).

Also Ammonia, Nitrite and nitrate testing is a good idea to ensure the levels
are safe
and 25-50% water changes once a week (depending on the testing levels).