Is it possible to group during competitive placement matches? It looks like the answer is "yes" based on some unconfirmed wiki and forum posts, but if so, how does it work? Can I group with players who have done their placements? Are there specific players with whom I can't group? (If this is answered in-game, I'm not near a computer.)
You can group with any amount of players during your placement matches or theirs, so long as neither person is in or above the rank of diamond.
Beyond that, in competitive, the only restriction on groups is being over a 1000 SR difference will not allow you to group. This is to avoid a diamond player boosting up someone in silver for example. Edit: As Kaizerwolf reminded me, at master tier the SR difference goes from 1000 to 500 between group members.
Otherwise you are free to group with whom you please. Just note that it takes a group SR average to determine who you play against, and you are also more likely to be paired vs other groups with similar SR averages.