In my opinion, the 14 CFR Part 1.1 definition of "Flight Time" establishes that a "Flight" (within the meaning of 14 CFR Part 61.109(f), pertaining to the Private Pilot Glider Certification requirements, for example), is when a glider, without self-launch capability (meaning Ground-Tow [auto or winch], or AeroTow), "...is towed for the purpose of flight and ends when the glider comes to rest after landing." (see "Flight Time" definition number 2 below).
I think the principle inherent in this regulatory definition supports the concept that in acquiring "flight time" you are engaged in a "flight." So, if you are required to have 20 "flights" in a glider, for example, any of the 20 AeroTow or Ground-Tow "flights" would begin with the tow and end when the glider comes to rest (see "Flight Time" definition number 2 below). With respect to a Self-Launched Glider, see "Flight Time" definition number 1 below.
Flight Time definition
(1) Pilot time that commences when an aircraft moves under its own power for the purpose of flight and ends when the aircraft comes to rest after landing; or
(2) For a glider without self-launch capability, pilot time that commences when the glider is towed for the purpose of flight and ends when the glider comes to rest after landing.
With respect to your other 3 questions:
- If I do an aborted takeoff after being wheels up, is that a flight?
If I had to abort the takeoff, I would not count this as one of the required "flights." I don't have an argument to support this, but it's just my opinion.
- If, in a self-launching glider, I take-off and land with never having turned the engine off, is that a flight?
After reviewing the "Private Pilot Practical Test Standards for Glider" (PTS) it appears that if your flight check is done in a Self-Launched glider there is an expectation that at some point after takeoff you will shut the engine down and land without power (it's the same PTS Area of Operation IV. Task Q., on page 1-16, that also applies to Ground-Tow and Aerotow). Therefore, in my opinion, if you did not "turn the engine off," you should not count that flight as a "flight" for the purpose of meeting the required 20 flights (from my example).
- If I do a touch-and-go with a self-launching glider, is that a flight?
In my opinion, my answer to your question number 2 applies equally to this question (I don't think it would qualify as one of the 20 required "flights.")
It's very unlikely that there are complete and unambiguous answers to your questions that would be accepted by everyone. But, my answers above represent my opinion based on how I view the applicable FARs and the PTS when read in context together.