Fish and inverts should be kept at an SG
of between 1.022 and 1.025 on a normal ongoing basis. If your tank is having a problem with ich then you want to leave it completely fishless (I don't know if that means the eel and pipefish or not) for at least 6 weeks, most now say 8. Raising the temp to 80 doesn't really hurt ich at all. It would need to be up around 86 (which I wouldn't advise based on your inverts) to speed up the lifecycle of the parasite.
If you're adding fish to your main without a proper QT
time there's a better than even chance (especially if you're using the same ol' supplier) that you're adding ich back to your main every time you add a new fish.
Fish in a QT
environment (without inverts, corals, etc) can have the SG
dropped to 1.009 or treated with cupramine if you do end up with ich again so that would be a big help in keeping it out of your main next go around (again, I don't know about the eel and pipefish's ability to withstand that so hopefully one of our resident experts will chime in. (Pipefish? Aren't they one of those fish that is usually in a species tank)?
There's a sick fish forum (which is probably where this post will be moved to) with lots of great advice on how to treat various ailments, including ich. They'll even be there with you every step of the way while your fish progress.
You've happened upon the best place in the world for helpful, friendly advice on how to care for your fishies. Welcome to AA!