for the first question: Adding reactions is pretty much like adding algebraic equations. In this case, you just need to equate the no. of electrons on both side of the added equation. So, what you do is, you multiply the second equation by 2. So the 2nd equation now becomes:
2Na ---> 2Na+ + 2e-
Now, if you add the two reactions, the result would be:
Br2 + 2Na + 2e- ---> 2Na+ + 2Br- + 2e-
now, you can canel the 2e from both the sides, giving:
Br2 + 2Na ---> 2Na+ + 2Br-
In case you don't balance the electrons, you have to write an 'e' with it's coeffecient as the no. of electrons in excess on a particular side. Like for example in this case, the right hand side would have had 2 electrons, and the right hand side would have had one electron. So, you subtract the LHS electron from the RHS electron and write e- on the right hand side. This is also fine:
Br2 + Na + e- ---> Na+ + 2Br-
In a reaction, charges on both sides are always same. In this case, the right side has one negative charge. Similarly the left hand side also has a negative charge [2x(-1) + 1 = -1].
So, both [c] and [d] are fine, but in case it is not a multiple answer question, you should go with [c] as in redox eqautions, electrons on both sides are always balanced.