Whenever I feel my patient's treatment is almost complete, I instruct them to scrutinize. I explain that while I know what I want, beauty is in the eye of the beholder. I don't want to take the braces off until we're both happy. I recommend you communicate your dissatisfaction with your orthodontist.Regarding your photo, are you biting down? If so, it appears that you have a bit of an open bite. Typically, you should not be able to see daylight between the upper and lower teeth when you are biting down.
Judging from the photo, it appears your lower front two teeth are touching at the incisal edges but as they converge towards the gums a space becomes evident. This is often called a "black triangle" in the orthodontic profession. Sometimes this can be resolved by filing between the teeth with a fine sandpaper strip. This will create a small space between your lower front two teeth that will then be closed with braces. As the space closes, the black triangle reduces in size. In my opinion, your upper front two teeth appear to be slightly out of alignment. Your lower incisors seem to be very close to ideal. The best plan of action for the lower may be to smooth the edges of your teeth with a fine bur. On the upper a slight adjustment bend in the wire may be necessary. It is crucial that you explain all of your concerns to your orthodontist. Do not simply hope that your retainer will fix your issues. This is unreliable and not likely to happen. In my opinion, most orthodontists are happy to make the adjustments you desire as long as you tell them what you want. Once the braces come off, the time and effort necessary to fix any uncorrected problems dramatically increases.
Yes, it is possible to rotate a canine 180 degrees. However, it will take a significant amount of time. The process would involve bonding brackets or "buttons" to the front and/or back of the tooth. Elastics would be tied to these attachments to help rotate the tooth. Periodically these brackets or buttons would have to be removed and replaced as the tooth rotated.
General dentists are legally permitted to do orthodontics or any other dental procedure they feel comfortable performing. Invisalign typically requires general dentists and orthodontists to get "invisalign" certified. This is a one to two day course. By no means does it make one an expert in Invisalign. It is important to understand that orthodontists do two to three years of specialized orthodontic training in addition to what general dentists do. Regardless of whether or not you see an orthodontist or a general dentist, it is important to ask how experienced with Invisalign your provider is.