Yep. Either your body is capable of controlling its blood sugar without any help, or it isn't. Diabetes can be controlled, even perfectly (or nearly), but it's still there. If you stop doing whatever it is that's keeping it under control, it will eventually pop right up again. Until there is a real, honest to goodness cure, once you have diabetes, you have it, even if you live to a ripe old age and have a full life—which, in this day and age, is perfectly doable.
As with everything else about diabetes, the answer is "it depends". Each person's physiology is distinct and individual and each may respond differently. One general thing to know is that alcohol suppresses the liver's tendency to release glucose, just as metformin does. So depending on what you are doing to control your diabetes, care should be exercised. Anything that might cause you to go low—medication, exercise, or whatever—can sometimes be exacerbated by the presence of alcohol in the system. So approach with care.
[See again the first two sentences of the previous answer.] You will get as many answers to this as people you ask. What works great for me may work either wonderfully or not at all for you. All the diets you mention have value for someone. Some are easier to follow, some less so. You have to determine this for yourself.
This is a really large topic and above my pay grade, so to speak. One basic rule of thumb to keep in mind is that for most people, aerobic exercise lowers blood sugar while strength training can often raise it temporarily.
This is a real hot button and can start passionate arguments. Regardless of which side of this you come down on, insulin is the most powerful weapon in the arsenal. Some experts believe you should start with it while others believe just as strongly that you should try everything else first. It's an endless debate; hang around here for very long and you'll see plenty of examples. [Full disclosure: personally, I am solidly in the "early intervention" camp.)
Where diabetes is concerned, the average internist is about as knowledgeable as the average GP. I emphasized the word "average" because you can always find exceptions, both good and bad. But that's the rule of thumb. Endocrinologists are the doctors who specialize in diabetes and are generally the most up to speed and knowledgeable. Again, exceptions aplenty. But a serious diabetes doctor is usually an endo. And again, it varies. Some endos concentrate their practices just on diabetes, some focus on other diseases, and some do both.
As for the second part of your question (what qualities to look for), here's my personal list. I want a doctor who knows where his knowledge of my diabetes ends and mine begins; someone who will treat me as a team member and not an errant pupil. We need to be able to communicate and we both need to be good at listening.