If I pick up the missions from past seasons, are they still viable for play? Could players play those, then use that karma to transfer to the new campaign? I just wasn't sure if since the season was over, if the adventures were no good anymore.

Season 1 is not really playable anymore, as it's SR Third Edition.

Season 2 and 3 are SR4 and are perfectly playable, though once you transfer or start playing in a new season, you cannot "go backward". So you can't bounce between Season 3 and season 2.

Thanks Willis, I had the exact same question. And of course, thank you Bull for providing the answer!