I had no idea this was so confusing, and I think what is hanging us up here is the language and usage. Patrick's answer is correct, but I think it still could be misunderstood because of the way he repeated back some of your statements.
Yes. Same answer as Patrick gave. A little clarification might be that they may give you one, or two, or more, depending upon the promo code you used. Everybody gets 1, but some who used promocodes that offered more may have additional "free" domains as part of their "plan"
Yes ... two domains, that is (one of which was free). If you use the free domain(s) that are part of your plan you will have a total of the number of domains you already own (registered anywhere at all, including DreamHost) plus the additional "free" one(s) that came with your plan.
No, not for "free" you don't. If you have not used the free one(s) you had as part of your plan, you can still add them, but they don't "add up". You will always have, at any given time, the total of whatever domains you have already registered and renewed, and the additional domains that came with your plan for "free", but they do not accumulate.
Nope. See question 3 above - you will still have whatever number of free ones came with your original plan.
Because you can't. You can only get another "free" one if you let the first free one expire (or any other combination you want, as long as you pay for all that you have other than the original number than came with your plan). You do get another free year of renewal on that "free" domain, and that continues as long as you have the plan or the domain - if you do not renew the domain then you are back to having another "free" one available.
Nope. You can get one whenever you want, and that will be your "free" one. If your plan comes with a single "free" domain (as most do) than that is all you will get, though you can keep that one and it will remain "free" (no renewal fees) for as long as you keep your hosting plan account with DreamHost.
Of course, you may not want to do that, as you may want a different domain, and no longer want the original "free" one you chose .. that's fine, you can just let it expire, and then you will be back to having "0" free domains on your pland, which comes with 1, so you can then add another.
Obviously, this could get confusing, so DreamHost just credits you with the amount of one of your registered domains each year .. that leaves you to sort out "which one is 'free' " in which ever way suits you.