The small boats that go WL/Contemporary/Ft. Wilderness start running about 6:45 am.
You can take one of those boats to the Contemporary, then walk over to Magic Kingdom.
The large cruiser that runs Wilderness Lodge/Ft. Wilderness/Magic Kingdom doesn't start till about 8:15-8:30.
The bus to Wilderness Lodge from the Settlement depot does start about 7, then you can transfer to a Magic Kingdom bus from there.
Also, if you would like some early AM exercise, there is a path from Ft. Wilderness to Wilderness lodge across from the petting zoo/stables, then you can catch the bus to Magic Kingdom.
Yes, the keys to the cabins are cards. If you purchased a package or purchased your park tickets from Disney at the same time you reserved your cabin, then your tickets will be on your room key. If you purchased your tickets separately and already have them in hand or have a "will-call" receipt, then your tickets can be placed on your room key if they have not been used yet.
Carol