I don't own an EBMM but my experience with other guitars tells me that it's not normal. Might be a fret-height issue. I'm sure Axis owners will chime in shortly.
Pretty much. I find this happens on all but one of my axis' particularly on the high register of my low E and A string. This sort of thing is normally a pain in the arse but on the MM guitars it doesn't seem to affect the amplifed sound. Whether clean or overdriven.
Edit: I play with medium to high action and more or less stick to factory neck relief.
what gauge of strings?
how is the action and neck relief currently set?
without knowing this, it's impossible to guess. pretty much all electric guitars with light gauge strings will buzz if hit hard. As long as its not overpowering the note when amplified it's probably a non issue. So many factors to consider too, fret condition, strings/set up, etc.
It is normal. The general rule is that if you cannot hear the buzz through the amp it is OK.
It is a tradeoff. Higher action with no acoustic buzz can give you one type of tone. Lower action with a little buzz gives you another, and may make it easier to play. Action and setup can be very personal.
I typically will set mine up right at what I call the "buzz" line (like a water line)!!! Meaning, the water may on occasion "splash" me, if it gets a little rough.