? 1. => TA is all alkalinity; Adj Alk is TA - alkalinity from cyanuric acid. (You also have alkalinity from borates, phosphates, and carbonates. CA is carbonate alkalinity.

? 2. => In one sense, the reading that matters is the one on your chlorinator cell. But, try doing the Aquachek again, but soaking the strip longer.

? 3. => If it's a concrete pool, yes. Otherwise, no.

? 4. => No, adding carbonate alkalinity will increase your pH; you'll have to add acid.

? 5. => I don't know that it's an INDICATOR of anything; it's a decent -- if slow -- method of dissolving CYA.

Regarding your pH -- learn to use muriatic acid. It's cheap, effective, and better for your pool. (But it has nasty fumes!) Here's the muriatic acid guide page.