Yes, they have self serve laundry and I've never had any trouble with the machines messing anything up. I believe when we were there last, it was $2.00/load to wash and $1.00 for 15 min. of dry time. My advice on laundry at any hotel is this: do it early in the morning or prepare to wait. The resorts shouldn't be that crowded during your time but for some reason, the laundrys always seem to be hopping. Just get up early and you should be fine. Either that or aim for the middle of the day when everyone is at the parks.
You can also send your laundy out although I can't tell you exactly how much it is, only that every time I've ever looked at the price sheet I've freaked out. So, to me, it's expensive.
ASMu may or may not be busy during your time frame. Early Dec. tends to be slow season for the resorts in general, but the All Stars get a lot of school groups coming through and it seems to me that the week you're there might be pop warner football time (someone else will know for sure). That adds a lot of people. They mostly stay ar sports but overflow to the music and movies.
You can rent the fridge for however long you like. Just tell them at check in what day you'd like to get rid of it and someone should come collect it. Just check your bill over closely before you leave to make sure they charged you accordingly.
I love ASmu and you'll have a great time!!!