he(?) should be fine with them,I have kept betta with many kinds of tetras.to fight ick you should raise the temp,I have a betta with ick(just rescued the baby from wal-mart)in a 3gal with a 25 watt heater and a 10-15 gal filter.its been a week and the ick is almost gone.
Bettas can jump. Our Betta jumped out of a very small opening in the back of our 10 gallon through a space beside the filter. Found him crispy and quite dead when I came home one evening. Lessons learned.
You can get it at Home Depot or places like that. Depending on how large of an area, you can probably get what you need for under 5 bucks. Grab a piece of generic acrylic sheet intended for a picture frame. You'd be better off with thicker than thinner... Thicker will resist warping.
Don't let them try to sell you an eighty dollar sheet of Lexan... You're just trying to keep fish from jumping out, not shooting their way out. LOL
BTW - there are millions (well, a lot anyway) of Bettas kept in various open top jars and Betta Bowls... I don't think jumping is a problem.
My thought - obviously like it's been said, try and just keep an eye on your betta's behavior. My betta literally beat up 3 neons (missing eyes, fins, etc.). However, Blue is a bad ***.