Not true. If you use calcium-containing antacids (like tums), you will get a good supply of calcium in addition to antacid effect. Other antacids (magnesium-containing, or so-called acid blockers like Pepcid (famotidine) or zantac) do not give you any calcium.
PROBABLY. The main reason might be that the amount of calcium in antacids is not enough to meet the required 1000 - 1200 mg/day recommended for bone health. As well as the need to take multiple antacid pills to achive this dose.
Not necessarily. I have understood that it is perfectly ok to use Tums for instance as a calcium supplement-- it comes in different strengths, including a 750 and 1000 mg strength (of calcium carbonate). What I had read was that your body cannot deal with more than about 500mg at a time anyway so I'm not sure the strength actually matters. It's important to take the calcium with meals several times daily.