Yeah - that's more or less what I saw in various videos - although it
appears that there are many, varied techniques that people are using on
these things that not everyone uses.
From your list (and from what I saw), it looks like the torch and the
tools are moved in all three axes - not just one...and with both the tool
and the gas jet having to move along the full extent of the X axis, you
have the problem of one having to cross over with the other (probably you
want two identical tools - one to the left of the gas jet and another to
the right).
It's not clear how necessary that all of this is though...it all seems to
depend on what your particular application of the lathe is. Most people
think in terms of a completely generalized tool - but probably that's more
than you strictly need.
But with just the inputs you're describing, this is going to be a
complicated and expensive machine to make.
-- Steve