Two questions and two suggestions

1.
Captain Marvel's interaction with the Avengers mostly happened off screen. As you said, they met her for the first time on CM's post-credit, this happened between the end of Infinity war and before she saves Tony.

If you think that her interaction felt awkward, that's because she wasn't supposed to be in the film, her appearance is forced by the studio. Many rewrites happened to accommodate her, which explained her awkward presences and her absences from most of the movie. She basically doesn't do anything significant in the story, without her the movie would still have the same ending, which is weird considering she is basically the strongest entity in the movie and should have a great impact on the story. The only exception to her insignificant is her rescue of Tony, but even that was a rewrite.

2.
There are many kinds of love, just like Thanos sacrificing her daughter to get soul stone doesn't mean she was his lover.

3.
Yes, Hulk story arc is unfinished. We get to see him beaten by Thanos on Infinity war, where he gets depressed and refuse to appear for the rest of the movie. Traditional storytelling convention would have him resolving that problem by confronting Thanos for the second time and if not win outright at least holding him down. But instead, we got "The Professor", who retain Bruce's mind but not as strong as the original Hulk, where his role in the movie is to be the one who snaps the iron gauntlet.

4.
Unclear actually, when he snapped the iron gauntlet Bruce actually tried to revive Nat, but he can't because Nat's soul is used for the soul stone. What this means is that there is actually a possibility that Hulk can at that point revive not only those died by Thanos's snap. And considering that Hulk was present when Loki dies, there is a possibility that he also revives Loki.