At the very start of a campaign, I might use the king in a few battles, but after a while I think it's better just to let him sit them out. Attacking with him may lead to unrest issues since he will get "stranded" after the attack if a siege follows.

As said before, groom the heirs. Once the sons come of age, send them into battle as commanders at every opportunity. This will make the heir a better king (and hence improve his children), and it will leave you with plenty of royal uncles with high command values.

As far as I know, stars on a princess only affect her resistance to assassination and diplomatic ability.