A few miscellaneous comments to add to recent posts. There has to be an external fill plug -- I was going to take a picture of mine but see you found it. Not sure what that internally threaded plug is for, actually. Is the hole possibly threaded for 1/2 pipe from both directions? If not, there should also be another drain plug. If you can't find it, I'll snoop around on mine and send a photo. You don't need a huge diameter fill plug, and if you drill it out you won't be able to use the correct filler fitting. It is nice to drain in more of a gush for the flushing effect.
For the motor, I 100% recommend going three phase with a VFD if you only have single phase, which accounts for most of us. You need low speed for threading, as Sasquatch has pointed out, and you also need some grunt at those lower speeds. A decent motor with VFD has that grunt, and a very low and sharp drop off of torque. You can also overspeed the motor to get spindle speeds higher than 800 you have now which you may quickly find you need for decent surface finish on small -ish parts which is what you are going to use this lathe for. A lot of Bantams seem to have come with a two speed motor and top spindle RPM double the 800 you are reporting. If you go for a fast 3 phase motor and use the VFD to access lower speeds, with torque, that may be the best compromise. FWIW, my chippie tops out at 3000 rpm spindle speed and I am finding myself more and more using the upper range speeds as I learn what the cheap carbide inserts that I run can and can't handle. It is not about saving time, it is about getting an insert to cut smoothly and break chips. This isn't limited to carbide, but more obvious when you use it. My slowest speed is 35 rpm in back gear. I usually fuss around with the speed when threading and often end up in the 50-75 rpm range for up to 1/2 inch diameter. Kind of the sweet spot for finish vs my nerves if the job involves a shoulder or tricky pull out without a gutter.
Before spending money sourcing a lot of replacement gears or paying to have them made, I would fix the obvious issues then pack it up and run it. A lot of lathes seem to work just fine with some pretty appalling looking gears -- they might be noisy but a slow speeds, you can live with it at least for a while and until you find the other gremlins lurking like alignment, bed wear, gib wear and etc.
Check that the shear pin (it must have one) is soft. Previous owner may have done you a 'favour' and installed a dowel pin or smooth end of a drill. While getting to know the machine, a brass pin might be advisable.
My understanding is that the Bantam was a very capable machine in its day, so that means to this day as well. Maybe not ideal for making aerospace parts, as they say, but very capable and worth the effort to save it and use it.