Prime Runner Missions (PRMs) are for existing characters with the qualifying amount of Karma Earned. They are not for new characters.
Convention Mission Packs (CMPs) are regular Missions, just set outside the main story locations. For example, the Season 3 2010 regular Missions were set in New York, but the CMPs for that year were all over the place - like one was set in South America. You should be able to bring a new character to them with no problem.
Also, for the regular Season Missions, once you play a later Season, you cannot play that character anymore in earlier Seasons. A character that plays the new 2011 Season 4 Missions set in Seattle cannot, for example, play in any more 2010 Season 3 New York Missions or earlier. So if you are planning on having a character play an earlier Season, make sure you play him all the ones from that season you want to play in, before hitting any later Seasons. The CMPs don't follow this rule, however - you can play those in any order.
-k
