Well, as mentioned they are too many to write them in a post, however you could check this link for some very important rules and, moreover, you could google whatever you want about the conventional rules of four-part choral and pianoforte harmony.
As for the second, I would like to make some remarks:
- In four-part choral harmony there is no restriction that two voices should not sing a fourth while the other two voices do not move, however, when such a passage is played on a piano, it sounds often too harsh to be considered classic, so it is to be avoided, due to pianoforte restrictions.
- The same - a little bit altered - applies to octaves and fifths. Should two voices move to a fifth or octave while the others do not move may, even in choral four-part harmony, sound a little bit empty, however, when played on a pianoforte, the result is usually very "cold", so, again, it should be, in general, avoided.
- Several other passages, such as thrids and sixths are allright to be used while no other voice is moving.
- In general, while parallel fourths are not entirely forbidden, many times they do sound really intense and harsh, which makes them not a nice choice.
- Except for parallel fifths and octaves, there are also their counter-parallel cousins. So, for instance, having Basso and Soprano moving from a perfect fifth to an octave (or another perfect fifth) with contrary move is also forbidden.
After all, what you are being examined to is music and it should remains so; if you write something that on the piano sounds nicely and is in context should be OK. For instance, I was taught that after a dominant (V) there should follow a tonic (I), however, I've used several times variations of an idea borrowed from the baroque - Haendel, specifically - that after (V6) one could have a (IV64) with a very pleasing result. So, despite all these rules, feel free to express yourself, as long as the given theme lets you do so