If it has a bad head gasket, or cracked head, it would,
1. Use a lot of Antifreeze
2. Yes, have air in the cooling system, and fill up the recovery system
3. May have white smoke in the exhaust
4. The temp guage would move a lot, as it would read liquid, one moment, and air the next.
There is a kit to put pressure in the radiator. This may not tell where the leak is, just if there is one, as it would not hold pressure.
A compression test can find a weak cylinder.
A leak down test can find a weak cylinder.
An additive can seal a leak, but may not help, if the head is cracked.
If the cooling system holds pressure, it should not boil at 230F or even 260F.