This^^, it assists the HVAC system in keeping humidity levels low in the cabin. This is why sometimes the AC compressor will run even though you are not in the AC or defrost mode.
Agreed. Could be as simple as corroded battery connections, or as complex as a computer module malfunction. You should take it to a shop/dealer to have it diagnosed.
Not necessary unless you get a check engine light telling you there is a problem. Then, this would be the first thing to try before replacing it. Unless you just like to take things apart and clean them.