Can I branch off of a 2 pole 30 amp 10-3 wire found abandoned in a junction box?
As long as the existing cable has a grounding conductor what you propose is absolutely fine, although you must replace the breaker with the proper two-pole 20A breaker. Although not required I would definitely place a label on the wire in the panel stating it is to be used for a 20A circuit maximum.

I would place the 10/3 in a box and branch off with two 12/2's going to your new loads. This will give you the two 20A dedicated circuits you are looking for.