Yes it can, when it works. Maybe this has something to do with the welder not doing anything...
Correct. The manual also specifies the breaker size.
I'm guessing the surge amperage is over 44, so they want a larger breaker upstream. You can likely get by with a smaller one (say, a 50A), but may trip it now and then.
For instance, my little 220V Hobart has a 20A input, but calls for a 30A breaker.
Just looking at the specs on mine, and then the specs for the various configurations of yours, it looks like the breaker specified is 150% of the input current.
Just realized yours is DOUBLE the amperage of mine! I bet that thing can melt some metal.