As I understand the system, it is not possible to have random people join you (or you them) for episodes of Spartan Ops that are a week or more old. The system only appears to let you join the current week's SO. However, if you have someone join your party you can take them with you into that older episode.
In regards to the second, if my understanding is correct, joining a game from that screen actually starts up a new game that will look for others to start a fresh level. I could be wrong about that one though. --- We want you...to join S.T.A.R.S.