This may well open a can of worms, but have a look at Rollie's Dad's method of lathe alignment,
It's essentially the same method I used, before I was even aware of it, where, in my case, I employed a 2MT test bar and a dial gauge. Because you are only using a clock gauge, there are no cutting forces to consider.
In my case I couldn't afford a proper certified test bar, but found a brand new, beautifully machined and ground 2MT extension sleeve for £5 from a government surplus store.
I used that to set up the twist in the bed, though using the screw threads on the Myford raising block, rather than sheets of paper. Because it's 2MT, I didn't even need to use a chuck.
I then added a 2MT stub arbour to the 2MT extension, which allowed me to set it up between centres, and was thus able to set the tailstock offset correctly.
When I then used the "dogbone" testpiece mentioned above, with a very light cut, everything came out closer than I could measure with a micrometer, albeit not a 10,000" one.
"Levelling" the lathe is advantageous, but not vital. I've no personal experience of it, but from what I can gather, it's more important with large lathes in industry where the sheer size can allow the bed to distort under its own weight, if the cast in concrete floor mounts aren't perfectly level. I this case the precision level is used across the bed, at both ends in the same way that a wood worker would use "winding sticks" to check for a twist in the workpiece.