So, How do I know how deep to cut the threads, when its deep enough and not too deep?
To answer the obvious question, I will make a threaded 'cap' to fit the tube. The cap will have external threads of course and I will have the tube to use as a gauge for the cap.
So, you've got this part solved, the cap (which you can see and measure more easily) gets done first, and makes a gauge for the internal threads, which are impractical to measure otherwise.
Making a non-standard thread without a gauge is not trivial. First, you have "theoretical" dimensions to work from. That is, the major diameter is is based on a theoretical "sharp" thread form. An absolutely perfect triangle with theoretically perfect sharp points. The root and the crest are both "truncated", or "rounded over". Thus the minor diameter is never actually the listed minor diameter, because the "point" in the bottom of the groove is rounded over. That means your tool "touches" the work, and you're already "some" distance in against the theoretical depth of cut. So if you go in the theoretical distance, you're too deep.
And the crests- They're given a theoretical height, but in fact it's cut short of that. Because this is custom, one of a kind stuff (or any thread if it's just regular tolerance stuff, general hardware type precision, then once you have your major "nominal" diameter decided (however random that might be), take your desired diameter, and reduce that diameter by 10 percent of the thread pitch.
For the plug, If I picked 28tpi out of your two choices (neither choice is wrong, I just picked one), that's 28 threads per inch, or 28 threads per 1000 thousandths of an inch. 1000/28 is 35.7 thousandths per thread. Ten percent of that is 0.0036. Call it 4. So your "blank" diameter would be four thousandths less than whatever nominal diameter you settled on. And the threads won't come to a "point". Dang friggen close, but not quite.
The same thing goes for an internal thread, except inside out. What you'd do in practice is work out (from your male thread), what the theoretical root diameter is, enlarge that "slightly) by the same three and a half or four thousandths, and start threading into that. And when it starts to look like a thread, but is not "quite" there, that's when you start with the cap that is also the thread gauge. Start screwing it in, see if it goes. When it's pretty close to going in, but "not quite", start with scotch brite or other abrasive, buff the nasties off of it. Those will greatly affect the fit of fine threads. And might easily take an "almost fits" thread all the way to a "fits good" thread.
Tip- There are all kinds of blogs and videos all over the internet telling you it's OK to polish internal threads with hand held abrasives. In some cases they're not "wrong" but there is a LOT of judgement involved that never gets discussed, and there's a lot of bad judgement. Your (approximmately) 7/8 hole... That's EXACTLY the right size to bind up between your finger and an abrasive pad or stick..... Don't do that one under power. Just don't. Hand turning the chuck is fine, but you could imagine, right.......
And... Presuming the thread boring bar is decent, not crap, not industrial.... Make the last SEVERAL passes at a small, but consistant infeed. Perhaps (if it'll cut this shallow) 0.002 on diameter/ 0.001 on the radius. Making CONSISTANT changes in depths gets CONSISTANT cuts. Driving in at 0.006 per pass, and trying to take 0.002 is difficult at best. Maybe part way in, play with the spring passes (repeating a cut at the same setting as the previous cut), to see just how far the tool is deflecting. It IS deflecting, the question is just how much. That last little pass when you're trying to cut just a whisker to free it up just a little... That's not the time to find out how much spring is in the bar, on this day, with this insert, in this material....
Actually I'm working on some hot rolled from the hardware store, just because it's what I had on hand.
That stuff is crap. Very useful crap, I've been known to get it on purpose, but it's crap. It turns very poorly. Expect that, be prepared with flexible or pad type abrasives to "smooth up" the surface. It'll make very functional threads (not structural, but very functional), but it wants a little babysitting during the process, the tool finish is not great. And of course clean up the little nasties before test fitting, as each and every little "ugly" is actually a raised bit of metal, that'll interfere with the fits of the threads. It needs to be dealt with (to whatever degree is practical for the intention of the final product), before test fitting, as a good fit with rough looking threads will be a loose fit once you smooth them up.