For Euphemia I can offer Walter Staghart as her baby dad. Augusta would have been born about a year after he graduated from Hogwarts. When I first joined the site I had intended for Walter to be the father of an illegitimate child but that plan fell through (never heard anything back from the player and as far as I can tell, they haven't active since I joined in Feb.) Thus, I'm all for him having an illegitimate child especially if he didn't know about it (and finds out in game in some way.) I also like the idea he had a fling with an older woman (though he may not have realized just how much older she was at the time).

Terence is the same age as Euphemia so they would have shared school years. He was Hufflepuff and Muggleborn, Euphemia could have teased him or treated him poorly as you feel is appropriate for her. He tended to be a bit of a loner in school but not weak by any account. He just did his best to avoid trouble. Either way, whatever their past they will both be teachers at Hogwards so will have chances to interact once school resumes.