The drive belt is slipping. The belt appears in good shape however. Do I have to replace it and if so what size is it as I have no manual or is there an adjustment.

Also, what kind of oil do I use in the transmission crankcase?

Hi,
Often there is a moveable idler if there is not a cable adjustment that will take care of it. Need some numbers off the machine to tell you about oil, though the most common by far is 90wt.
Peace,
Clarke