What do the different sellsword companies do in between contracts? Would they own land or castles to stay at whilst they wait for employment, or would they spend all their time basically as an army on the march?

Well, sellsword companies would try to minimize that downtime, because they don’t generally have lands or castles to provide them with income when they’re not fighting. So when not employed, they tend to spend their money rather quickly, which is why mercenaries so often become bandits.