When you make peace with a country, an automatic 5 year truce is started with every country that was in the war. You can fight wars against other countries in that timeframe, but violating a truce (starting a war against one of the countries you were just at war with before truce expires) comes with a ridonk hit to your stability (-5? I don't even remember, it's bad, never do it).
And yeah, manpower is one of the big balance changes between EU3 and EU4 - manpower used to replenish pretty fast in some cases, now I think they said it takes 10 years on average.
The cool thing about Venice's navy is that you aren't stepping foot in their capital province anytime soon, since navies block land bridge crossings (there are a handful of paths around the world where land armies can cross between straits without the aid of ships, like the Bosporus, or Denmark<->Sweden, or Italy<->Venice, but hostile navies in that sea territory will prevent you from doing it). As such, while you can take provinces from Venice, you will never break them without a strong navy of your own.