Well, first I'm going to recommend reading all the info on your cruise line's website or to call them directly. Advice you get here may help, but will not be definitive. I guarantee that every question you asked here can be answered by browsing their website.

In my experience, here are my answers to your questions:

1) Do you mean 6 people from 1 family in 3 cabins? One credit card to pay for all? If so, you should check in together. Check-in time varies by cruise line and embarkation port, but your boarding documents should already have this information for you.

2) Any cruise I've taken, you are allowed to disembark after initial embarkation and then re-board without waiting in the long check-in lines. But again, this is one to check with the cruise line.

3) You can always go to the port, check in your luggage, and then see more of the city before you personally board. That's the safest thing, but maybe not the most convenient depending on where you're staying in relation to the cruise terminal.

4) There have not been limits on any cruises I've been on, but I tend to cruise in the highest suite cabins so the rules may be different. In general there's not a lot of storage space in cruise ship staterooms, so people don't want to take a lot of stuff. There's not a lot of room for clothes, nor is there a place to put lots of empty suitcases!