When is a 100-hour inspection required if alternating commercial and private use?
This FAA legal interpretation covers a lot of scenarios and it looks like it answers yours too. Although it refers to rental, not ownership, the result is the same because rental time isn't instruction or carriage for hire.

First, what the regulation says (14 CFR 91.409(b)):


  Except as provided in paragraph (c) of this section, no person may
  operate an aircraft carrying any person (other than a crewmember) for
  hire, and no person may give flight instruction for hire in an
  aircraft which that person provides, unless within the preceding 100
  hours of time in service the aircraft has received an annual or
  100-hour inspection and been approved for return to service in
  accordance with part 43 of this chapter or has received an inspection
  for the issuance of an airworthiness certificate in accordance with
  part 21 of this chapter. The 100-hour limitation may be exceeded by
  not more than 10 hours while en route to reach a place where the
  inspection can be done. The excess time used to reach a place where
  the inspection can be done must be included in computing the next 100
  hours of time in service.


The key phrase from the interpretation is this one (my emphasis), which really just restates the regulation in a simpler way:


  if [you are] going to operate the aircraft to provide
  flight instruction for hire, then the aircraft must have had an annual
  or 100-hour maintenance inspection within the preceding 100 hours of
  time in service.


Now we can compare your scenarios to the ones in the interpretation. I won't quote the document here, but scenarios 1 and 6 together cover your cases.

In the above scenario, does the 10 hour window even apply to the owner? He's flying his plane solo, not for hire, so in that capacity he should be able to fly it as long as he likes.

Correct. If the aircraft isn't going to be used to do any paid instruction or carry paying passengers then he can fly the aircraft himself, rent it out, lend it to a friend etc.

What if the owner in the above scenario teaches out of his plane for 100 hours after the annual, stops teaching and flies his plane personally for 50 hours, then decides he wants to teach in it again? Can he get a 100 hour check to get the plane legal for commercial use?

Yes, in fact he must. The aircraft requires a check within the last 100 hours of operation to be legal for flight instruction for hire, or carrying paying passengers.

Is the next 100 hour due in another 50 hours? What if instead he flies it personally for 100 hours after the 100 hour is due? Does that mean he has to get two 100 hour checks done in a row to use it commercially again? Or does he have to get a full annual to reset the 100 hour clock?

The 100 hour clock is reset by a 100 hour inspection or by an annual, he doesn't need a second check. But note that if the CFI does get an annual, he still has to deduct any 'overtime' from the 100 hours:


  You may perform an annual inspection rather than a 100-hour
  maintenance inspection when the aircraft reaches the 100-hour
  limitation under§ 91.409(b). However, if you perform an annual
  inspection on an aircraft that has exceeded the 100-hour limitation,
  you are still required to subtract the excess time from the next 100
  hours of time in service.


As for going over the 10-hour excess time, the interpretation covers an equivalent scenario (scenario 6) where the aircraft is flown to 112 hours legally by renters, inspected, and then used for paid training again. The explanation is poorly written in my opinion, but it confirms that the aircraft needs an inspection before any paid training can take place - which makes sense - and the next inspection after that must be made within 88 hours - which makes less sense.

Extending that forward, it would mean that if you fly to 199 hours, you need an inspection - either 100 hour or annual - to make the aircraft legal for paid training and the next inspection would then be due in 1 hour! I don't know if that's really the intended result of the interpretation because it seems to conflict with the regulation's wording about "within the preceding 100 hours of time in service". And what happens if you rent the aircraft out for 299 hours before using it again for training?

Maybe I'm just misreading or misunderstanding things completely, but it looks like the interpretation leaves a couple of loose ends and the only definite, official way to get them answered would be to ask for another interpretation.