The bottom pic definitely looks like a strangler fig (a ficus). I know that because, when I lived in Miami, one planted itself next to my avocado after Andrew. Like you, I thought it looked viable but you need to get rid of it. It was a real bear to remove and lived up to its name. It will take over everything above and below ground.

Link to bay laurel (laurel nobilis). https://en.wikipedia.org/wiki/Laurus_nobilis

To my eyes these leaves maybe a species of fig (Ficus) (?) not the common fig (Ficus carica). However with out flowers it will be difficult to narrow down it exact genus. For now check out species of Ficus from this included link below, click on image to enlarge. Perhaps you could give us an update when this is more mature. Again I’m only speculating. Best wishes! https://alchetron.com/Ficus-aurea

Do the leaves smell like bay?