My basement floor is wet with sweat from the line set going into the air handler. Anything I can do to stop the water on the floor?
put a drip pan under it and a drain for the condensate to escape
Insulate the bare copper.
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How many times must one fix something before it is fixed?
I'll also add a footnote to what Beenie said. When you insulate the copper, DO NOT put the lines together an insulate both (you don't want the small line in direct contact with the larger one. You only have to insulate the sweating line.
Is basement conditioned space?
Did you think about a dehumidifier for basement?