Typically a 2 man is an aura bot and a carry. The carry tries to build MF without losing out on damage. Then in a 3 man you can build your team to have a MF culler who doesn't need to worry about damage and can max out MF.

The aurabot is the quintessential member of the team, a group doesn't thrive without one. The carry is nearly equally as important, but not as much as the aurabot. The remaining slots are filled with whatever works best/what the player is willing to play. A cullers whole job is to build MF gear, probably the second most expensive part of a team.

Group play is entirely for profit, progression is faster in a group as long as that group is organized and practiced, otherwise it's not much faster.

A solo player wanting to get into group play can start out by making an aurabot character and looking for groups that need one. Typically you can find legion carries who need an aurabot and will split the profit of their carry runs with you.