I second the firefish as it tends to swim near the top and all the mandarins I've seen seem to prefer the bottom (never had one, so this is just observational).
Sounds like ich to me too, but i'm very much a newbie on diseases. Do a search on Ich here on the site and read mikeguerro's (I probably misspelled it...sorry Mike) fight with ich. Very insightful.
If on the likely chance that the landlord doesn't pay you maybe your home insurance will cover it. I don't know if you have that coverage but it's worth a check, two full tanks is pretty pricey. Sorry to hear that nothing survived.
Three fish may be pushing the limit on the 5g....just go slow and watch for changes. I'm sure many people have done it, just let your tank adjust to each new inhabitant before adding more.
The anemone thing may be a bit overambitious...JMHO.