I believe you can buff by spending 200 coups/ingots. It's at the top of the page. And that buff applies to the entire team, meaning everyone will get the buff. But one person would have to spend the 200 coups/ingots.

One of them increases power and something else ( i forgot) and the other decreases the defense and resistance of the summon (serpent).

So it is better to be in a team as it will benefit everyone.

You can do summon capture on anytime of the day even when you missed the schedule on the day of, but you have a 30min timer or limit once you enter the summon capture instance.