My first instincts were that he's either a reincarnator/trasmigrator like her, or he's a regressor. The latter could fit wirh his question at the end, if we're to presume the two were potentially romantically involved in the past (at least based off the prince's behaviour).
It would make sense to me, she was the only princess of marrying age and would likely be matched with someone of a similar social standing = 2nd prince, for example. Maybe something happened that motivated him to go study abroad from a young age.
Who knows! I'm just puttimg a theory out there lol. There's a third potential of him using magic or something that would've expected a specific reaction from her, ie. echanted item (--> explains his infamy as a womanizer despite his lack of skills). Tbh I think my first theory is more interesting, but this is also v plausible. Granted, this manwha isn't great at showing instead of telling, typically doing "showing AND telling", so it's not really great at displaying subtle suspicion in a character's actions/mannerisms/behaviour. So either we have "trust MC's gut" with her line of saying she's unable to read him when she's usually good at reading people, or "MC's imagining it" and he's actually more sweet and has genuine interest in her. Guess we gotta wait and see ╮(￣▽￣)╭
Curious to know why the second prince asked her that question. I thought he might have transmigrated like her, but his question “you don’t feel anything when you see me?” (I’m paraphrasing) threw me off.