Just remove the batteries from the plane. I like to fire up my engines then empty the fuel tank then fire up the engines again to run out any left over fuel.
Here is where you will see a lot of other ideas. I run Powermaster fuel that has some castor oil in it so I don't bother with putting in any after run oil. Some do and some don't. I live in a very dry area so I have never had problems with rust. Others swear they must add after run oil. If you live in a damp area then by all means use it, doesn't hurt to be safe but the only engines I have ever had a problem with I used after run oil.
Covering a plane isn't a bad idea but it's only dust and comes off when I'm ready to get them back up. If you want then go ahead and cover them up. I leave in my gear, no reason to remove it.
If after storage your engines are stiff just heat them up with a shrink gun to soften up the castor oil that has hardened. This does happen but if you run them dry I haven't had the problem.
As for your house, I have several friends going through the same thing and there are a lot of folks in my area having the same problems. Hang in there!! It gets better in time but it's sure no fun !!!