It is unfortunate that a tooth moved into the implant area. From what your situation sounds like, the best treatment option would be to move the teeth into the correct position. I don't have radiographs or pictures to review to see if there are other alternatives, but other alternatives are likely to be a compromise and may cause more harm than good.
It appears you have an extra tooth and need to have it removed. You would also benefit from orthodontic treatment.
However, if vodka does have a pH of 7.5 and there is no sugar in it (which causes bacteria in your mouth to excrete acidic byproducts), then the likelihood of that causing tooth decay under the Invisalign trays is very low. If you were to drink vodka with your Invisalign trays on, I would at least recommend removing the trays at some point and rinsing with water.
It doesn't appear that additional orthodontic treatment can correct your concerns. It looks to me like your teeth are in a good position, and to be honest, they look really good. Everyone's teeth have a slightly different shape, and you may be wanting to look like someone else. Your lateral incisors are slightly smaller than your central incisors and they look proportional. They are also slightly higher than the central incisors, which is ideal. You also appear to have a very nice smile arc. I wouldn't recommend changing anything. In fact, I wish more of my patients had teeth that had the shape of your teeth. Count yourself lucky!
I agree that it appears that you have lip incompetence that you may not have had prior to orthodontic treatment. If you had a lot of crowding before braces, the only way to fit everything in without extractions is to expand the arch and procline the front teeth. If this is done too much, lip incompetence can occur. In order to correct the lip incompetence extraction of premolars, or possibly orthognathic surgery such as a Lefort impaction, would be required. Additional pictures and radiographs along with a physical exam would be needed to determine the best course of treatment for you. Mouth breathing at night it not good and should be addressed. I would recommend going back to your orthodontist, or seek another opinion.