Are romances gated to story as in the OT?

Yes. You have to proceed through the main mission, and in the case of squadmates, do loyalty missions, to unlock parts of the romances. And yes, they do 'lock in' at a certain point (which then locks you out of other options) but it happens later in the game and the conversations where that happens seem to be pretty clear.

Whether just hooking up with a character locks you out of a romance with another seems to depend on the characters, or how far along in that romance you are.

As for flirts... 'three' seems to be the magic number. You can freely flirt with any character up to two times without it meaning anything, but three turns it into an actual romance even if you skip some. Though it won't 'lock in' until that conversation I mentioned earlier. No names, but... I slept with one character, did the three flirts but was not yet locked in, and was propositioned by another and could've slept with them too. Didn't take it though, so I'm not sure if there would've been any consequences to doing so with either character.