>If it was nosema can that be passed on to new bees if I put them in that hive and they eat the honey?
Yes. If it was, then it can. There are spores in the feces. I'd clean it up with clorox or vinegar if you're in doubt.
>How long do I have before wax moth moves in? We are still getting cold nights (upper 30's) and a lot of cold days (mid 40's) here in Portland Oregon.
It depends on how long and cold your winter was. Here after a normal winter I usually don't have wax moths in any numbers until about June. But the last couple of mild winters they were bad in May.
>How should I store these frames until I need them for new bees or a swarm?
The freezer would be the most sure thing. If not, then keep them closed up so the moths and mice can't get in and they should keep until you can distribute them to other hives.
>or should I let the strong hive just rob the honey out of them?
Better to put them on the strong hives than let them rob them.
Any issues if I drop an early swarm in this hive?