Rambin (you need to set up your signature),
1-1/2"-8 is most likely what it is. But you don't need a thread pitch gauge to confirm it. Lay the scale shown in one of your photos down on the spindle nose, with zero in line with the first full thread. Another thread should appear in line with every 1/8" mark on the scale. And the major diameter of the threads should be 1-1/2" or up to about .005" less when measured with a caliper set.
There are a lot of different ways in which they are done on various brand lathes, but there are two basic steps on almost all lathes to switch from Direct drive to Back Gear drive. Step 1 is to take the machine out of Direct drive. Step 2 is to put it into back gear drive. To go back to Direct drive, you reverse the order. Step 1 is to take it out of Back Gear. Step 2 is to put it back into Direct. It sounds as though you are skipping step 1. Some machines have a lever for each step. But in your case, I think that I see the head of the direct drive pin in your 6th photo showing the spindle nose and bearinbg. The pin goes through a hole in the bull gear and into a hole in the right end of the spindle pulley, The pin has some sort of spring loaded ball detent in the bull gear that holds the pin either IN or OUT. If there isn't already one, make a mark on the right rim of the spindle pulley and in line with the pin. Pull the pin toward the tailstock until the ball clicks into the second detent. You should not be able to turn the spindle freely, without turning the motor. Now do Step 2.
Before you run the lathe in back gear, find and remove the oil screw from the spindle pulley. It is probably in the OD of the 2nd or third pulley step. Squirt SAE 20 into the hole, replace the oil screw, and run the lathe in back gear for about 10 seconds. The first time that you do it, repeat the steps twice. After that, oil the pulley bushings every day that you use back gear or once every 6 months or so. And oil the back gear bushings with the same frequency.
I can't help with the pulley size.