I just cleaned mine with dish soap and water. Just don't submerge any part in the water. An alcohol wipe or bleach/water wipe would probably be fine too, if it's rinse and dry it really well.
I had eggs in mine when I ordered the cover and got it before I locked down, so that's when I installed it. I think folks have shown a piece of plastic mesh, rubber banded or zip tied in place to cover the fan, or pretty much anything you have on hand that will still allow uniform air flow but close down the size of the gaps. Someone even made a webbing from just rubber bands tied together.