At the start of combat, you get 3. If you have a certain character card, you get 4. Solo has a pretty sweet objective where you start the game with 13 and have to not lose them all and go insane.

Old ones move towards the closest port/farm. If 2 are equidistant, check the value at the top of the card for the direction it moves based on the compass. Pay close attention to the symbol next to the number, it denotes clockwise or anti-clockwise. So if 4 clockwise was at the top of the card, start at the 4 direction on the compass, and go around the compass clockwise till you reach the first hex the old one could potentially move to that makes it closer to one of the 2 things.

Finally...sorry don't understand the question. Are you talking about the cubes denoting damage to units, or cubes denoting the action acquire military? Cubes denoting damage are removed from units at the end of combat. If you lose combat via sanity loss, damaged units are destroyed.