Oh right, so I guess republic also prevents royal marriages... wasn't there some sort of option (was it demand annexation or offer vassalization or whatever it was) that required a royal marriage or I'm wrong on this one? And if there is, how does it work with republic?
And legitimacy always stays at 100 for republics, right?
Almost, but not quite. Noble republics can make marriages, but can't get or have PUs due to the lack of a dynasty. The other republics cannot, but in exchange have several other advantages.
The lack of a royal marriage, as you point out, is that you can't offer vassalization - but you can annex vassals you already have or gain by force.
Legitimacy doesn't exist for republics, so thrones can't be claimed and it gives neither bonuses nor penalties. Due to that, all republics have +1 tolerance to heretics and heathens - an effect monarchies gain by having 100 legitimacy instead.