1. It is possible to play power card the way that it is only discarded (and no power used) ?
2. Can player look at his own illegal contribution (face down money card) ?
3a. Can accountant move only one card (other one is moved back) ?
3b. Can accountant move card to politician where he already has 5 cards (and discard one of those to make room of course) ?
1. On p. 10 of rules, you may play a power card without using its power.
2. On pp. 9-10, yes.
3a. Not specifically in rules, but I would say "yes" because you are picking them up and putting them in any location.
3b. Not specifically in rules, but I would say yes because you can discard money cards to make room for new ones.