The Pearl Fisher village chief (the village south of your mainland landing) offers his daughter, Tayanna, to become my wife. I've been courting (well, been nice to) Isabela de Yruenes who joined me on Hispaniola (starting island). Is it possible to marry Isabela or perhaps someone else? What effect does marrying her (fully or only their way) or declinging do, other than her joining or not joining the expedition?

Is the potential love interest the amazon babe? Because I turned down her offer (happily married guy) and I'm wondering if that's it or there is another one later.

Yes she's your love interest if you're playing a male character. You need to take her offer, then take the priest's quest to kill her, tell her about it, kill the priest for her, then she'll be able to join you and you'll be able to play out the romance (which is basically 2 more conversations).

Personally I felt she was a bit of an odd choice for a romance option considering she's a "hidden" character, pretty much the hardest one to recruit.
Isabella would have made more sense imo, but I guess since players can choose to skip Hispaniola and just start in Mexico after they finish the game once (this is bugged atm, you need to manually activate the option in the ini file), the devs wanted to have a romance option you could always choose to have.

The respective female love interest goes the same way. It's Coyotl (or how he is spelled) the Eagle Warrior the aztec merchants want you to assassinate.