Another question. Is it preferable to stay smaller so you can change laws easier, speaking as duke of Apulia. The previous run it seemed to me that the bigger I was, the harder it was, so I am thinking about playing small until I revoke Council powers.
Also, what happens when you give land to your kid heir with 0/0 demesne size?
Also
Do I really need the Pope opinion about me to be good as Apulia? Can I move to Free investiture if I go kingdom?
I would
never give land to my heir unless they are married and have already produced a child or two. And even then, it's not something I will do unless things are desperate. (Like if I am trying to hold on to a huge amount of extra land towards the end of my life.) Once you give land to an heir, they are free to make decisions, and those decisions will be stupid - stuff like dueling and getting maimed, taking terrible focuses and acquiring awful traits, attacking and usurping vassals you like, handing out favors like candy (which you will need to pay back later), etc. So again, do not give land to your heir.
Related to that, the 0/0 demesne size you see listed is for someone who has no land. Give someone land, wait for the month to end, and they will readjust up to the new rank you gave them, increasing their capacity. (Baron, Count, Duke, etc.)
Changing laws is basically the same no matter what rank you are. You get some additional options at King and above. But just keep pushing towards what you want from day one.
What
will make changing laws easier is not size, but how long you rule and how much your counselors like you. As time goes by and you develop positive traits, your council and vassals will all love you. (Take Theology focus or Benedictine/Dominican Order if your traits suck, those will give you traits that make you very popular.) On your council, stack as many Content-type people in there as you can. Mentor your heir and stick them on the council. It takes a few years but at some point it will all click into place.
I like Free Investiture once I have the rest of my realm laws in place, but it's not the end of the world if you don't have it. The Pope will like you more and will ask you early in your ruler's life to change it, but if you have otherwise positive traits then you can refuse without issue. If you have a lot of negative traits then you may get excommunicated for refusing. It's good fun to groom bastards as super-priests and future cardinals/popes. It's also very effective to recruit high-Learning, same-culture courtiers and nominate them to your vacancies.
Related to that, and this is a bit more advanced, in any Kingdom, I recommend aiming to have at least one vassal Archbishop (Duke-level theocratic vassal) and one vassal Merchant Republic (Duke-level burgher vassal with coastal access). The Archbishop can be where you stick your most loyal, highest-piety nominees, and they'll likely end up being Cardinals and future Popes. The Merchant Republic is a huge moneymaker. Both should also become go-to council members for you. (Just don't put your Court Physician on the council because then they won't do any medical work.)