Use the die to clean up the threads, after you get them close.
Ok it has been 45 years since trade school and cutting threads on a lathe. If I remember correctly the half nut has to engage exactly on the numbered line. As far as the roughness of the cut try some of that heavy cutting oil used for black iron pipe. Good luck
Ed......the only thing I have run into that may have caused your first issue is the stock slipping in the jaws or possibly getting bumped between passes.For problem #2......I would guess that maybe your sfm is on the slow side. Hard to say. It's normal to want to turn the spindle slow when threading due to the "rapid" disengage that is often necessary, but I get much better finishes running as fast as I can and being very quick on the disengage......lol. If you are threading into a shoulder, you can cut a relief at the end of the thread to give you a bit of leeway on the disengage.Mike
I don't know about your lathe but some lathes you can not disengage the lead screw while cutting metric threads. What RPM selections do you have on your lathe?
Ricky made a very good point, if your lathe was not designed as a "metric" lathe, engaging and disengaging the half nut is a game if chance. I have used small engine lathes most of my life, and on small critical parts, I have turned the spindle my hand. RPM can and will eat your lunch, if you can't control the spindle.Threading makes a lot of tool pressure, especially on a small lathe. Typically, my last 2 or 3 passes are made without advancing the compound rest, this relieves the tool pressure and improves the thread finish. BTW, there is no substitute for a good cutting fluid that keeps a buildup from forming on the cutting tool. Keep the tool overhang to a minimum and avoid allowing the work to flex.BobH.
You said you have a thread relief. If you have a bar for threading ID's use that. Thread from the back side starting in the relief and thread coming out in reverse. This will allow you to run the RPM you need and be able to stop the chuck to manually run the chuck forward to get the tool back to the thread relief.
I cut a lot of shop made taps from O1 and your main issue is is speed. For 3/8 O1 you should be up around 900-1000 rpm.Give it a try on a piece of scrap. The difference in finish will be day and night. What's happening right now is the material is tearing off. Have a look at it under a strong magnifying glass and you'll see the tears.I know the thread chase is whipping past like a Ferrari but one of the other posters gave you a good tip. Flip the tool upside down and run in reverse. Then your not threading to a stop ....which can be real intimidating at first.