1) If you press
F1, you are sent to a menu in which if you press "
Profiles" you will be shown the cast of romance-able characters, that if you subsequently
press on one of them it will display your relationship status. Said relationship status, works on a depleting criteria and is comprised of 3 phases: platonic (initial relationship state) and romantic or sexual states, depending on your approach. As for the relationship bar, it will deplete and send you to the next phase. The progression is seen with the white bars that start appearing when you have made a correct choice.
2) GD (the developer) has stated that there won't be a harem ending, so there's no point in romancing more than one character (at the moment). Although in some of his replies in Patreon, he has considered the possibility of allowing to romance/conquer more than one character.
3) No idea, if there are any mods for the game it might be a bit pointless since there's too little content at this time and there isn't any reason to mod the game for now.
P.S:
Prima in english is
cousin, just so you know