can cargo captured the previous week be held over and delivered the next contest period the following week?

Yes, theoretically. But it's difficult to keep the cargo for the week other than in the cargo hold of your ship. You can't dock to any other station when holding the cargo.

Yes it can, but like Ray said, it has to be kept by a player, which poses a problem when keeping it around for more than a few hours or so. Another option is to stash it in an empty sector and pick it up once every < 15min to keep it from disappearing.

Generally, if you're carrying over cargo to the next week, it's cargo looted from convoys a few hours before the round ends on Saturday.

I know draug used to leave his dent or xc on with a bot that his guild members could use to drop off ctc for it. Which worked well unless the server restarted or he somehow lost conenction.