Eggshell calcium, buffering vitamins

OK, a long time ago I read about taking eggshell calcium and a comfrey mouthwash (I think) to help with your teeth. You were supposed to dissolve the eggshell in vinegar, but I can't use vinegar, so I tried bottled lemon juice, and it didn't work very well. I shelved the idea, but have been collecting eggshells. I now have a big jar of ground eggshells. I am trying to follow the Iodine protocol, which favors magnesium (which I also haven't been taking, because I can't afford magnesium citrate and I ran out of magnesium bicarb which they seem to dislike for no stated reason). I live in the country and have hard water, so I kind of wonder if my water has magnesium in it. Apparently hard water is where the ancients got their magnesium from.
I am thinking of starting the magnesium bicarb again, since I can't figure out what is wrong with it, and surely it is better than nothing, but I am also thinking about trying the eggshell calcium, if only to see if I can dissolve it in something. Maybe if I take both, it will work out OK. I am on a low carb diet, so I don't think I get a whole lot of calcium. I understand that the calcium in milk is not in the cream portion, so butter, sour cream, and the like are not helping me in the calcium department.
So what I wanted to know is if dissolving the eggshells in vitamin C (which I have a ton of due to a sale and my attempts to follow the Iodine protocol) would work, and how would it affect the absorption of the C. Has anyone done this before? I am really unclear on the affect of "buffering" on the absorption of vitamins in general. Also, what happens when you take calcium and magnesium at the same time. I know vitamin manufacturers must think it's OK, since they sell "cal/mag" supplements, but what actually happens in your body?