The MIT team is primarily student, but faculty, staff, and spouses are also eligible to join. It’s fairly common to come into it as a social activity, but those who are primarily looking for a social outlet tend to migrate to the Ballroom Dance Club, which is a social group (started sometime in the 70’s, I believe). The Ballroom Dance Team is focused on competition. But the team does definitely have social events and is a collegial environment. People are very supportive of one another whether or not they are dancing together. (Many people are surprised the first time they go to a ballroom competition, because they expect some sort of refined gathering. The couples on the floor may look elegant, but the people on the sidelines cheer louder than they do at football games.)
The dancers choose their own partners, and switching partners from one competition to the next is common, especially among the rookies. Instructors will offer advice to those looking about prospects, but no one is required to dance with any other particular person. Partners need to be not only physically compatible, but to have similar working styles and preferably similar learning methods. If I’m trying to help people on the team find partners, I probably spend more time thinking about their personalities than I do about how they will look together.
The unusually tall women and short men often have difficulty in finding appropriate partners, but certainly can be competitive. I remember a couple of foreign students who were about 6’6" and 5’11", respectively - we used to refer to them as the “German juggernaut,” because it could be pretty scary when they started coming down the floor at high speed towards you. There is one guy who has been on the team for years who is exactly five feet tall. He has a lot of trouble finding women who feel comfortable dancing with him, but he’s quite a good dancer and does well in competition.
It’s hard to say what the ideal height matchup is - for standard, it’s probably more important that the partners have about the same length inseam than that they be the same height. There is more height flexibility in latin, because the partners spend less time in closed dance position, and even when they are in “closed” position, they’re not usually in body contact.
Both men and women can start out with regular shoes, but those who compete seriously almost always want to get one or two pairs of shoes made for ballroom dancing. The most noticeable difference is the sole - ballroom shoes have soles of chrome leather, which is chosen because it has a high static coefficient of friction and a low dynamic coefficient of friction - once you’re moving, it moves across the floor easily, but when you’re standing on a foot, it grips pretty well. Ballroom shoes are also more flexible, so that you can really bend the foot at the ball, and then push strongly out of the toes. Finally, the women’s shoes have a steel shank, so you have to really work hard to break a heel. Ballroom shoes typically cost about $100-$150/pair, so people don’t buy them until they’re pretty sure that they want to dance seriously - but they’re not that much more expensive than a good pair of oxfords.
Actually, the most common reason for men to start is to meet girls. 
The MITBDT is very unusual among college teams in that we usually have an excess of men, not women, in the rookie classes. It’s still less than the percentage of men at MIT - the women are more likely to want to dance than the men - but the team stays pretty balanced. Some are dragged in by their girlfriends, but those couples usually end up in the social club, rather than on the competition team. There are plenty of ballroom couples who are also couples in “real life,” but it can be pretty complicated maintaining a personal relationship and a dance relationship. (My husband and I danced together for a couple of years, but it was starting to have negative effects on our relationship outside of dancing, so we both found other dance partners.) In terms of romances that start up between team members, I would say that they are about equally split between partners that start dating and nonpartners. I would say that getting into a romantic relationship ends up destroying a dance partnership about half the time when it occurs, either because the dance partnership is sacrificed to the “real” relationship (like me and my husband), or because the dance partnership cannot survive a romantic breakup.
Maybe, but I wouldn’t remember without a name.
(Incidentally, in amateur competition, “Senior” starts at age 35. :rolleyes: “Senior II” is over 50. In pro-am, the age categories are more finely divided, and vary from competition to competition.)