You can only gain points in your own category your registered with. Person with Cat 3 team keys can't gain points for kills in a Cat 4 team.
If others in your team are in same category they can get points also, points are given to the player not to the team name as no-one owns a team name. Pretty sure it is done this way because MA has to award to someone the items and everyone in the team is not going to get one of those items it is just 1 of each for whole team not each person in team.
You have to plan your team accordingly, hence the term team. The whole team is competing for those prizes so you have to organize a tank, support, healers etc. and that tank which should out DPS all others in team should get the points and be trusted enough that when he gets the items from winning he will share the items or at least the ped value of the items won with the team members.
If you don't trust your team leader like that well then your not really part of a team so to say.
However solo has different rules which I think are f*cked up rules but MA has them written that way and allows all kinds of crappy unfairness workarounds for points but oh well that's the way MA roles I guess.