The friendliest place on the web for anyone with an interest in aquariums or fish keeping!
If you have answers, please help by responding to the unanswered posts.
Tetras can be nippy. I don't have experience with red eyes but my betta is in with cardinals, five banded barbs, ottos, two mollies and a guppy.
There was an initial 'settling in' period where the tetra did nip his fins but they lost interest after a few days. That was 3 months ago and I've had no problems since.
Make sure the betta goes in last so that it's not "his" territory he needs to defend and have a back up aquarium just in case. I have 5 bettas and 4 of them have tank Mates of snails neon tetras guppies glass catfish the one that can't just has a 5gal because he will kill anything in sight.