For (d), from the working you can work out a case whereby the statement does not hold (i.e. p does not divide 2b). To disprove, it is easiest to have a+c be a prime number (divisible only by 1 and itself e.g. 2, 3, 5 and etc). Say we choose a+c=13. Then we need to choose a 1
For (e), work out case by case and you will find that the statement holds.

For (f), the shortcut is to notice that you can use the results from (e).