Chemistry - Calcium carbonate toxicity
Solution 1:
Looking at the Material Safety Data Sheet (MSDS), most of the issues with it seem to stem from the physical consequences of it being in fine dry powder form. This means that if you get it on your skin, it can get into cracks and pores and easily dry out your skin to the point of cracking, and will cause irritation or worse if you get it in your eyes, for example. It's not toxic if you get it on you, though -- rubbing a lump of limestone against your skin isn't going to do anything except abrade it.
So, yes, if you're working with the powder, wear gloves. And safety glasses. And long sleeves. (See also: lab coat.)
If in doubt, follow the MSDS.
Solution 2:
It's essentially chalk. I'm not aware of any longitudinal studies of gymnasts' long term exposure to powdered calcium carbonate, but my sense is that the worst that can happen is your skin can get dry and irritated. If you have a part time job as a hand model, you will want to be especially careful to avoid skin contact.
If you're in a lab, of course, it goes without saying that you should take necessary safety precautions such as proper eyewear and skin protection as well as a lab coat.
Solution 3:
So far the skin questions have been answered nicely. Here's the ingestion:
used in antacids—yet there are warnings about ingestion
half of the problem is the acid neutralizing capacity: your stomach may like to keep up its acidic pH.
The other half is of course how that neutralization happens:
$\ce{CaCO3 + 2 H+ \rightarrow Ca^2+ + H2O + CO2 \uparrow}$
You'll produce lots of carbondioxide gas in your stomach