Answer 1

Impossible because different operands may result in the same value.
Can you determine x in the equation x * 0 = 0 ?

As you say, 3 | 5 is 7.
Likewise,
3 | 4, 3 | 6, and 3 | 7 is also 7.
So if 7 and 3 given, the other operand can be 4, 5, 6 or 7.
No way to determine which is the original.

You can list all possibilities instead, but I don't think it is what you want.