At first I wondered where these questions come from, but I see now, one can ask if Terra does have any special interest in Aqua in first place, a person who he trained with, grew up with and so on
Regarding the first question, I often think it's just how female characters are (too) often portrayed as motherly figures, caring, protective, with unwavering faith in those they consider important or dear to them. This often includes mandatory affection/attention towards people not exactly worth their time, as you said. In some other fandoms, there were similar discussions and some people mention that, in Japan's case, there is a preference for this side of femininity to be shown in a female character, in pursuit to make the character really, really likeable or loveable. Strong females who give zero f*cks, on the contrary, here in KH end up like... Larxene? (talking just about original characters, not Disney ones or so). But if we talk about the interest or lack of interest Terra shows towards Aqua we'll return to discussing how lacking and unfortunately simplistic BBS's writing overall was, and how the character relationships suffered from this, despite us still being generally able to enjoy BBS as a game.