You may be familiar with Hydrochloric Acid, but it doesn't really sound like it, or you have a very different risk calculation than most of us.
But to answer your questions:
1) You should drain your tank of seawater before adding the acid. While acidic saltwater would still work to dissolve calcium carbonate snail tubes, coralline algae, etc..., you're asking for a huge foaming problem as the initial acid works to neutralize the saltwater's alkalinity.
2) 1N HCl is far too strong for what you're planning on - circulating it through your tank in a living space. 1N HCl (which is about what you'll get by diluting concentrated HCl 1:10) is still quite dangerous - it will violently react with calcium carbonate, will burn your skin, eyes, and mucous membranes, and having 220 gallons of it inside your family room is extraordinarily risky.
3) You can spray vinegar if you wish, but vinegar is quite slow at dissolving calcium carbonate. It could well take 10 or more applications and few days to accomplish your goals.
The best solution to your problem is to simply disassemble the tank, sump and plumbing, get some friends to help you move the tank outside, and wash it out with 0.1N HCl (with face and hand protection).
If you insist on not moving the tank, the safest thing for you and your family would be to make 1N HCl outside by diluting concentrated HCl 1:10, and adding 20 gallons of this to your 220 after you've filled it with tap water. Doing a two-step dilution like this will drastically cut down on the hydrogen chloride gas that will otherwise fill your house, and be somewhat safer in the event of a spill.