There are regular universe X-Men and some from the ultimate universe. Both are identified by Xs. The Brotherhood of (Evil) Mutants, their enemies, both in the regular and ultimate universes are identified by a red helmet, a representation of Magneto's helmet.
This is usually true. The X-Men all have an X inside a circle on them. The Ultimate X-Men have a red X on them. The Brotherhood you have right on. There is one version of Magneto that is X-Men however.
I'm not sure if this is true with the X-Men, but there have been cases of team abilities being not on the dial even though we know they are on a team. For instance, Jay Garrick Flash from Hypertime is missing the JSA team ability.
Also, sometimes characters are given a team ability even though they are not a member. This was done just to give those teams an ability and to use alternate team abilities. This is can be seen with the Alpha Flight and Thunderbolts getting the Avengers team ability, Squaderon Supreme and the Gaurdians of the Universe getting Defenders, and the Doom Patrol getting Outsiders. With X-Men there will be Exiles, Excalibur, and X-Factor mixed in here as well. There are also members of the Hellfire Club that have the Brotherhood team ability. Those two team abilities are kind of just a catch all for good and evil mutants.
In general the team abilities in clix are not always the most useful tool for judging who is with which group.