I've been keeping bettas many years and have never had any of the problems Ty described.
Ghost shrimp are usually harmless enough, though the Betta might eat them.
Some bettas do enjoy a current, some don't. Unless you have a ridiculously large filter in the 3 gal, you shouldn't have to worry about fins getting sucked into the intake. They are very strong swimmers.
Bettas are pretty tough, so with frequent PWC and good ominorvious diet, it will probably live a nice long life. I feed freeze dried blood worms and live brine shrimp.
Enjoy, they are a lot of fun and have a lot of personality. I really enjoy them.