It sounds as if your doctor has appropriate training and board certification for the procedures you want. That does not mean he is good at them. Make sure you see photos of his results first.
It is important to consider credentials when choosing a surgeon for aesthetic surgery as there are lots of "pretenders" out there. Plastic Surgeons are certified by the American Board of Plastic Surgery and are trained to perform surgery on all parts of the body, face, and breast. Facial Plastic Surgeons are ENT doctors who have done one year of additional training and are certified by their Board to operate on the face only. Oculoplastic surgeons are ophthalmologists who similarly have done one additional year to perform surgery on the eyelids and brow. Dermatologists are trained to do skin lesion removal and closure, but have expertise with fillers, peels, lasers, and topical products that most surgeons do not have. The American Board of Cosmetic Surgery is not recognized by the American Board of Medical Specialties.
The surgeon that you are referring to here is board certified in their specialty and fellowship trained in cosmetics. That is exactly what you should be looking for.
Always make sure you seek a dermatologic surgeon, oculoplastic surgeon, facial plastic surgery or plastic surgeon who is board certified and fellowship trained in one of these core four cosmetic specialties.
Beware of the general surgeon who is masquerading as a "cosmetic surgeon" but has done no extra time training in a cosmetics fellowship.
These credentials are excellent. Many surgeons may have great credentials, but that doesn't necessarily make them a good surgeon. However it does show at least good training and education. So now you have to evaluate what you think of their surgical skills by having a consultation to see if you have good rapport with them, to see if you like their suggestions, and to look at pre and post-op photos. Also ask to speak to other patients who have had surgery done.
If they are a member of ASOPRS they should be an excellent choice for any eyelid surgery. Some ASOPRS members also have training in facial surgery and can do excellent facelifts. For a nose I would only see a member of AAFPRS.
This surgeon has likely is qualified to do the kind of surgery you are pursuing. His experience and reputation are important to consider as well One good way of determining if a surgeon is qualified is to ask them if they have priveledges at a hospital to perform the procedures you seek.
The short answer is Yes he is well qualified but make certain you and he have good interaction.
However, the credentials are simply not enough. You actually have to carefully assess the work of the surgeon. You have to interact with the surgeon during the consultation to get measure of the surgeon. Some surgeons are natural born salespeople but you want to decide if the surgeon makes sense to you. What you are looking for is a mesh between the qualifications, the manner of the surgeon and their office, and the results they show on their website. If you need ptosis surgery, it is improbable that you will find a surgeon who is going to do both a great facelift and a proper eyelid surgery. Oculoplastic surgeons do facelifts but not many of them. Facial plastic surgeons do eyelid surgery and some also dabble in ptosis surgery but very few turn out great ptosis surgery. You may very well need two different surgeons. You are asking the right questions.
These are all impressive credentials and certainly speak to this surgeon's dedication to the craft, but what may be more telling for you as a patient are before and after photos on their website and your own personal impression of them. It is vitally important that you as a patient feel comfortable with whoever you entrust with your surgical procedure to attain your desired results. I'd go ahead and book the consult to have the opportunity to meet them in person. Best of luck to you in your search!