What do “regions” do

I would go with option one. You say that it leaves you less profit, but that is only partially true. Since you will eventually die and play as your heir, all of that money will drop right back into your pocket. It is possible that your heir will waste some of it, but not a large amount. Most of the money he earns will go back into his properties, and so that gold will end up benefiting you in the long run.

As an additional bonus, if/when your heir wins the war, he will get money and prestige from your non-heir vassal.

The main purpose of Prestige is to add to your Dynasty Score: this shows how powerful and successful your dynasty is. If your final Dynasty Score is higher than your buddy's Dynasty Score, you're a better ruler than him. You are usually going to get a lot more Prestige than you can spend over the course of a ruler's life.

That said, there are a few things you can spend Prestige on, though none of them are particularly expensive, unless you're a new ruler of a young dynasty or otherwise poor in prestige:

1. Creating an Antipope costs 500 prestige.
2. Marrying one of your kids to someone of lower rank than your kid reduces your kid's prestige; it costs -100 prestige per difference in rank. Marrying a commoner with awesome skills can be worth it, but those skills had better be good!
3. Fabricating a claim costs around 150 prestige, in addition to the gold required to bribe the locals to "remember" some facts about your claim.
4. A White Peace (if you're the aggressor) or surrendering a war will cost you some prestige, but you don't need to have prestige in those cases.

Though it's not an action, remember that you get an opinion bonus of +1 per 100 prestige, that applies to everyone. It caps at +20, but it's still quite useful!