OOOOkay, let's take these one by one.
Part 21 says that you have to have PMA (Parts Manufacturing Approval) for ANY part a company produces and sells for use on an aircraft. It does NOT specify which aircraft it goes on. It is simply a license to PRODUCE (manufacture parts) and sell them as airplane parts. One major exception to this rule is 21.303(b)(2) which says that any OWNER can manufacture parts for their own aircraft.
An STC is an approval to change the way that a particular airplane (or series of airplanes) is modified but remains in compliance with the Type Certificate under which the aircraft is manufactured. It is a MAJOR change to the way the airplane left the factory. Since it is a MAJOR change, a 337 form is required that references the STC and how the change was made in compliance with the STC.
Close - actually any modification is a change to the type design and any Major change to a type design requires approved data (minor changes only require 'data acceptable to the Administrator'. The S in STC is a hint - Supplemental Type Certificate. Once an STC is incorporated, the aircraft (or appliance) no longer conforms to the original TC, it now conforms the the original TC except in those areas where it now conforms to the STC... An STC is one method of obtaining approval for the data associated with a major change, an 8110-3 (which is issued by a properly delegated DER) is another, FAA Approved Service Bulletins are another...)
A 337 can also be used as a field approval for MAJOR modifications (the definition of MAJOR is how an airplane flies, operates, or is changed from the flight characteristics listed in the POH or other published operations data (like the owner's manual for elderly airplanes)). The FAA goes on to say in a few Advisory Circulars (see below) how a mechanic can determine MAJOR from MINOR, but the overall responsibility for this determination is the INSTALLING MECHANIC. Now, the clever INSTALLING MECHANIC goes to the INSPECTION AUTHORIZATION mechanic who is going to do the next annual and they jointly determine which is major and which is minor. Minor is simply signed off as a logbook entry.
14CFR Part 43 actually lists those things which constitute Major repair/Major alteration, but it is laughable and it is indeed the mechanic performing the work's responsibility to make the Major/Minor determination. As an aside, Part 121 carriers are required to develop their own Major/Minor policy which is subsequently accepted by the FAA. generally, the Engineering department of the airline is responsible for generating the policy and the engineering department necessarily falls under the jurisdiction of the ACO, but the FSDO accepts the policy. Can be a great source of consternation, but I digress.
The FAA has issued a series of Advisory CIrculars "ACs"(which are non-binding opinions of one or more divisions of the FAA) on how stuff ought to be done. NON BINDING, but disregard them at your peril.
Advisory Circulars are absolutely non-binding, you cannot be punished for not complying with an AC unless you claim to have complied with it and did not in fact comply with it, but that falls under the auspices of falsification of aircraft records. In FAA speak, an AC "provides a means, but not the only means, of complying with a regulation... they do not create or change a regulatory requirement... (they may) contain explanations of regulations, other guidance material, best practices..." You may absolutely disregard them, but in general they do prove rather useful and painless - AC 43-13 being the greatest example - compared to developing your own means of compliance. Another aside - Part 121 carriers and OEM's routinely develop their own means of compliance but most GA folks have neither the technical prowess nor, perhaps more importantly, the financial resources to develop their own means of compliance. Not to mention the associated liability...
A TSO is a Technical Standard Order. A TSO references a non-FAA document produced by an industry consortium (that's a bunch of guys sitting around the table) that says that if you want to build (for example) a TSO transponder it has to put out so much power, it has to have so much sidelobe suppression, it has to work from this temperature to that temperature, it has to survive the following shake-rattle-and-roll regimen, and a whole bunch of other stuff. Now you have your choice. Since the FAA (in their infinite wisdom) have chosen to write most of the FARs that stuff must MEET the TSO rather than BE TSOd, you can sell your stuff as MEETING the TSO. Getting the TSO means that you submit all your test data to the FAA, wait until the first virgin of Spring has been sacrificed,and then MAYBE if Jupiter aligns with Mars you will get the TSO approval back in the mail the following millenium. Maybe.
The whole "meet the TSO" is an interesting, and I personally believe, legitimate loophole. Worth noting that NO ONE may approve a change to a TSO'd product other than the TSO holder. In other words, you can't do anything to a TSO'd product except as specified by the OEM - Major/Minor, doesnot matter. Which brings up an interesting point - that requirement does not apply to an article that MEETS as TSO, it only applies to TSO'd articles. Hmmmm.
I stand ready to defend my thesis ...
No particular reason why I selected this post to make comments other than that it was fairly well organized and speaks to several things with I am intimately familiar. Just pitching in to try and help clarify this mess that the FAA has created. It amazes me how much I don't know - I am an A&P/IA, FAA-DER, pilot and have been working in the capacity of aircraft mechanic and/or Engineer (Mechanical by degree, Aerospace by practice) for damn near 40 years, yet I constantly have to dig into the regs to try to figure out yet another issue that I am confronted with. In other words, I ain't throwing any stones here and I damn sure don't know it all. I do keep learning more every day and that's what keeps me going!
Jim