First note that you must comply with BOTH federal AND state law, whichever is more restrictive, not one or the other. I have no idea what MN state law is on SBRs, so you'll have to check it in each of the following cases.
But, as a starting point, for compliance with FEDERAL LAW ONLY, let's look at the AR15-type questions first:
I own an AR-15 rifle. I believe I cannot legally remove the stock and replace the barrel with a 10" barrel.
I believe that is right. The receiver must BEGIN it's "life" as a "handgun" configuration in order to ever be legal to convert to a handgun. Once a rifle (receiver), always a rifle (receiver). You CAN change from handgun to rifle, but you cannot change from rifle to handgun, ever, IINM. So even if you put take the buttstock off, this is no bueno. That's why if you ever buy "blank" receivers, you're always better off buy ones marked or designated handgun - that way you can make them into EITHER a handgun or rifle, at your whim, without any NFA paperwork. But if you buy "rifle" receivers, you can make rifles only.
Now suppose you made a regular rifle from a handgun designated receiver. So far, so good. But then suppose you wanted to go BACK to making it a handgun. Could you do this? I think the answer is technically "No you're not supposed to, because 'once a rifle, always a rifle', and you created a rifle". BUT, as a practical matter, if the receiver is marked handgun, there's no way the BATFE could ever know (nor would they care I don't think) that at one time you made it into a rifle for awhile.
Now you CAN however, make or "manufacture" an SBR from that regular rifle, by leaving the buttstock on and filling out the NFA form, sending in the $200, and waiting for the background check/approval, and THEN add your short barreled upper. Which is obviously far more useful than an AR "handgun", anyway. But takes $$ & hassle.
As for the T/C question:
If I can do this to my Thompson, then what's different about the two to make it legal?
IIRC, I believe the answer is "Because the BATFE, in all of its wisdom, carved out a specific (nonsensical) exception to the general rule, very narrowly, for the T/C family of guns only." Someone please correct me if I'm wrong.