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Can the NPDA constructed to accept L, such that L = L1 U L, L1 = {1n 0n | n > 0} and L2 = {0n 12n | n > 0} be drawn like this?

This is an informal representation of NPDA. Is this correct?

Or should the NPDA accepting language L should have 2 final states?

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CFL is closed under union and both L1 and L2 are DCFL so L is CFL.

Now second point is ,your rough state transition diagram correct or not. No its NOT correct , in this diagram you considered L1= {0n 1n | n>0}