@aegisheart That is a lot of questions.
First, I am in the minority but not alone in disliking the term "gifted." Probably what you are observing is precoscious development in some areas. It is awesome to support this--it doesn't nesessarily mean that it is something clearly separate in approach--it just means you may need to meet the child where they are.
It is perfectly reasonable to address a child as a small person and to allow them to grow into a relationship where they can reach for a level where they have not yet arrived. But you should also be fully aware that, say, a developed vocabulary or spatial awareness, etc., is not necessarily paired with emotional maturity, high executive function, or the like. Different humans, different levels.
I don't think anyone reputable will diagnose ADHD or similar at that young an age, given executive dysfunction is pretty much what being a three-year-old is about.
I guess the point here is that the labels are less important than the specifics: giving your child an environment in which they feel safe and cared for, and are exposed to manipulable objects and experiences that enrich their experience. This is as true of "gifted" children as it is of those who are "normal."
My parent ignored outside advise about giftedness resisted efforts to move me up in grades until I was about 11. I had undiagnosed ADHD, and teachers generally thought of me as potentially bright but unmotivated. Like most students I was just bored to death at school. I took some standardized tests that year, and had the opportunity to attend some programs for the academically precocious,. I started taking university courses the following year.
The advantage to having access to a peer group that was similarly precocious is hard to overestimate. On the other hand, the "gifted" label is often a curse, and one that is, I think, fairly harmful to young people coming up with a self-image of what they are good at.
My sons have tested as "gifted" and one has quite profound ADHD--which unlike mine is treated. There are reasons to understand differences in kids' behavior. But more generally, I don't think it matters. If you talk to someone who has been specifically trained to teach gifted kids, they will provide a whole list of accomodations: if you listen carefully to these, I dare you to find one that wouldn't improve the learning of any student, with any background.
So: pick a good environment. Provide interesting spaces for exploration. Select your early schools wisely (and if you don't know where to start with this, select a Montessori school). And just enjoy parenting your kid, however brilliant and frustrating they are on a given day.