Reasonably well, with one catch. Studies comparing fortified plant milk against cow milk have found broadly similar calcium absorption, but calcium carbonate is insoluble and it settles into a sludge at the bottom of the carton. If you pour without shaking, the last glass carries most of the calcium and the first several carry very little. Shake it properly and take it with food, since the carbonate form needs stomach acid to dissolve.

At antacid and supplement doses, yes, and both are predictable. The carbonate reacts with stomach acid to produce carbon dioxide, which is the belching, and calcium slows transit, which is the constipation. Long-running antacid use can also produce acid rebound, where acid output climbs once the tablets stop. None of this applies to the milligram quantities used as an anti-caking or firming agent in ordinary packaged food.

It depends entirely on when you take it. Calcium taken with a meal binds dietary oxalate in the gut so less of it is absorbed and less reaches the kidney, which is protective. Calcium taken between meals has nothing to bind, and supplement use in that pattern has been associated with higher stone risk. This is a genuine timing rule worth getting right rather than a reason to avoid calcium, since low-calcium diets make oxalate stones more likely, not less.

No. In the UK it is a legal requirement: white and brown wheat flour must be fortified with calcium carbonate, so it is in most non-wholemeal bread whether or not the bakery chose it. It contributes no gluten and no trigger of its own. If bread reacts with you, the wheat, the fructans or the preservative are the places to look.