There has been criticism of the film that many of the female characters, especially the female characters in the 1920s, seem to fawn over Gil and constantly go on about how great a writer he is (even though what we hear Gertrude Stein read aloud is...OK at best). But if you interpret Gil's travels into the 1920s as at least partially his fantasy, it makes perfect sense that he would imagine himself to be well-liked and fawned over by his idols. He's basically living in his own personal idealized fantasy, except instead of winding up in Rivendell and being added as a tenth member of the Fellowship, or being sorted into Gryffindor and becoming BFFs with Harry, Ron and Hermione, he's showing up in Paris and becoming besties with all the great writers of the 20s.
This is supported by the fact that when he and Adriana travel to the Gay Nineties, which Adriana loves, Adriana is the center of attention and is adored by the famous artists of that time, thus indicating that they're now in her fantasy.
Dali's comical obsession with rhinos may be a reference to his sculpted rendition of the famous Dürer's Rhinoceros.
Adriana and Gil part ways in the 1890s; while she seems happy to remain, it’s possible that she could change her mind, and because she doesn’t know how to get back to her own time, she could be trapped in (what is for her) the past.
To be fair, Gil never really knew how he got back either the first few times. At the very most we see him walk away from the action with a sort of "it's time for me to go back" mentality, and he just ends up back in the modern day with no way back to the '20s until the next night. There may be some limits to going back (it has to be the same night or it can only happen at night) as seen by the fact the detective was in the palace in the daytime. But if she did end up stuck, Gil wouldn't really be at fault on this one, since it's unlikely he could tell her how he goes back even if she asked.
The last we see of the detective is in the 17th century where he is being chased by guards and will likely be caught and executed, and none of his family, friends or coworkers will know what happened to him.
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