2) there is not one
3) confusing question but sounds like u r asking if u can power something requiring 120vac from the 100v side. sure
there is no nuetral when u have 2 wires coming out of a transformer; just 2 wires. u can call one nuetral if u want, call it L1 or L2. whatever.
reread and it sounds like u r not going to remove this xfmr from ur machine; just want to tap into it for 120v to feed a 24vdc power supply. so yes, just wire across the 100v side with 2 wires that go to the 120v input of your power supply. dont ground either, just hook them up and dont worry about n vs L noemclature.
sometimes msch builders tie one side of 120v to machien ground, so if u care, yes, put ur meter from machine case or ground to each side of the 100v and see if one is 0 volts; if so it is the 'neutral' side. other would show 100 v to ground.