The Eva-dry Mini Dehumidifier does all this and more! (said in my best infomercial voice)
Actually, I don't know if it does all of this and more, but there are lots of happy Amazon customers that say it does.
There is no power while it operates and no cords to plug in. Once full, just plug it into an outlet and allow time for the unit to dry it's silica gel crystals. It can absorb approximately 8-10 ounces of moisture and should last around 10 years.
I've just ordered 2 of them, so I'll report back in a month or two with my findings.