Congo Tetras grow to about 3 inches and will eat almost anything you can give them. They also should be housed with rainbows and other large species so i don't know if they would work with ones you have now. They prefer temperatures of around 77 degrees farenheit. Congo tetras should be placed in a planted tank if so they will thrive.
Also, the smallest amout of tank they shoooould be placed in is 21 gallons. So your tank is fine, but with the other fish I can't predict what will happen. Congo Tetras prefer to be in schools, and not 2-3 like 5. But you might get lucky, I would give it a shot. Be on stand by to see if anything happens.
Hope this helps!
The problem is that congo tetras are best kept in a school, and since they grow to about four inches or so (and I've seen a few that were larger than that), you need at least a 40-gallon tank for a school of them.
The other problem is that congoes get big enough to eat your neons.
That would depend on a lot.
As for fish compatibility, you're fine. Though when the ram gets bigger it will bully the tetras.
8 neon tetras 8"
3 otto cats 6"
Which means you're at about 18" of capacity. and have another 11" to go.
I'd go with 8 congo's. :)