You could had verified that yourself by going to the hangar and check, or you can go to your pilot profile and click on your History tab to see what, and if you received a bp.
But yes it is right, the one that pic up the bp gets it, but everyone gets the mission completed.
As serebus said, the crystal what you pick up in a squad is divided by all squad members,
but the reward for mission is always individual, so if no one in the squad has made it before,
everyone get the reward pay + experience aka xp.
Now about missions and Story Missions, someone who doesn't have an SM (story mission) or a White (Standard Mission) in their list yet, they will not be able to join the squad,
they can only if it is visible at their mission list, or if they have completed it already,
but then they will not receive anything for it anymore, as once received when they completed it.
For Story Missions and White (Standard) Missions
There is a restriction with ship and tech for every system, off course system rares are allowed.
Vega with Vega ship & tech (Vega rares)
Antares with Antares ship & tech
Gemini with Gemini ship & tech
Mizar with Mizar ship & tech
So you cannot install tech from eg Antares to a Vega ship cause it will not permit you to start any mission.
PM aka Pirate Mode = Pod Me aka PVP mode aka Player vs Player kill mode.
This is of your own risk, if you decide to put on PM, you will be seen like a red cloth held at front of a bull.
This is a pirate game, so try to remember the risks u want to take or not.
A few advices to Newbs.
