Apparently in the U.S. most of the Type Ratings are actually carried out by the airlines/operators, or on behalf of them by independent training organizations.
No, but why would you go spend six or seven thousand dollars here and there to get a type rating, without a job? Let the employer hire you and pay for the rating; if the employer wants you then the employer should be willing to invest the time, money, and effort to train you in their equipment.
Corporate and charter operators typically require a six month to one year commitment in exchange for a type rating. It's equitable.
This means that to a large extent, what is actually entered in the licence of the individual pilot is a function of what the airline/operator wants to include (PIC/SIC rating, or none at all if no international flying is involved) as they paid for that training, and they don’t want to give away anything more than what it is strictly necessary.
What's on the pilot certificate is a function of the training the applicant has accomplished and the practical test he or she has taken. If only a SIC practical test is given (not much, if any difference typically between a PIC or SIC checkride so far as maneuvers), then a SIC type is awarded.
Apparently the FAA doesn’t have much to say in this process either, FAA just enters in the licence what it is requested to by the operator, not the pilot, as long as it complies with FARs, of course.
Why would the FAA care? The FAA processes what paperwork is given them. So long as an applicant has met the requirements, then the FAA process the form 8710 for whatever privileges are requested. The Federal Aviation Administration isn't about to confront an employer and tell the employer they're making a mistake, give this guy a break, he really ought to have the full type. It doesn't work that way.
Can a pilot do a Type Rating on his own, without an airline/operator?
Sure. For anywhere from five to forty five thousand dollars a pop, you can go get type ratings all day long in anything from a B744 to a DC-3. It's your money. Of course, you come out of the type with a fresh temporary certificate, no experience in type, and no job...so you've just tossed away your money. But if it's worth it to you to dump your life savings for an endorsement to legally fly one specific make and model, then have a ball. In the US, buying a type rating is generally considered somewhat of a disgrace, with some exceptions. Let the employer pay for the type rating. The applicant comes to the table as a fully certificated professional pilot with years, often decades of experience and sacrifice. If the employer wants a quality applicant, let him invest the training cost to train that applicant in his specific equipment.
If he can, how would that be entered in his licence?, would he apply himself to the FAA, or would it be the training provider who would?
Such training is nearly always done through a designated examiner, rather than the FAA. The examiner signs off the certificate and issues the temporary, and the applicant never sees nor talks to the FAA during the entire process. Training facilities such as Simuflite, Flight Safety International, Pan Am, and others, provide training in the classroom and simulator and issue the type rating upon successful completion of a practical test at the end of the training...typically three to six weeks.
So far as what's entered on the pilot certificate...if you trained for a type rating, then the type rating is on your certificate. The particulars depend on what you desired when you started your training.
What would actually be entered in his licence, a PIC or SIC rating?
As nobody in their right mind would pay out of their own pocket for a SIC type rating, then the applicant is going to put in the effort, time, and expense to finish the training with a full type rating.
Is an FAA SIC Type Rating on a FAA CPL accepted to work as an FO outside the U.S. for a non U.S. airline/operator, namely in Asia, Middle East, Africa, South America, etc.?
It should go without saying, but save for some utility jobs, most operators are going to want to see the ATP...not just the commercial certificate.
With respect to who will hire you...that's entirely dependent upon your qualifications. That said, if you obtain a type rating in a B744 in the hopes of getting hired into a B744...the operator is going to expect you to be able to show some proficiency and understanding with the B744. Lacking that, you've merely added a few words to your certificate, with no experience to back it up. In some cases, the rating is enough, but most operators out there are going to want to see at least five hundred hours in type, along with the type rating.
The few places that accept just the type do so because they're too cheap to invest the money, or have such an inadequate training program themselves, that they can only take on board type rated applicants. In those cases, you're usually better off giving the place a miss.