First, just for the record, I am (among other things) an electrical engineer.
1. Some delta connected three phase (most?) have one phase wired with a neutral to provide single phase. I can draw a schematic if you want, but basically at the transformer one of the phases is center tapped, and that center tap is then used as a neutral (and connected to ground.) I suspect that is where he's getting the single phase for the rest of his garage.
2. There are many uses for auto-transformers. Yes you can buck/boost with one. You can change voltages (for example, 120 to 240 or versa-vica!) You can also hang one across an isolated (not grounded) 240 source, center tap that auto-transformer, and then ground that center tap. You will then get 120 volts on each side of that center tap. Nice thing is that if the 120 volt loads are reasonably load balanced that transformer doesn't carry much current, and things get very efficient.
So we need to ask the OP the question: how is he getting that 120 single phase for his shop's utility use?