Does the dent from burr holes after brain surgery ever go away? What about from bone flap reattachment? Do scars ever disappear completely?

Nope. Depending on your age burr hole cavities may nearly completey fill in and may not be noticeable but will never completely go away. The same can be said for scars as depending on your age and genetics the scar may become very small but no matter who you are they never become exactly like the tissue prior to injury.
Depends. Usually if there is a burr hole, there is some sort of 'dent' if a plate was not used over the hole. In skinny patients this can be prominent. However, hair usually grows there and one can no longer see it but can still feel it. The scar doesn't go away completely. All the best!