Nope, doesn't count for Scrabble, despite the validity, it has to actually be listed in the dictionary, and the official Scrabble dictionary, sadly, is the wholly lacking Merriam-Webster's.

I'd say it's not necessarily grammatical, but as a well-established idiom, you don't sacrifice clarity by using it. It's similar to the expression "full well", as in "he knew full well that writing 'eaxct same' was ungrammatical, but his point was still made.

Tmesis is part of a larger linguistic process known as infix. Infix simply involves adding a morpheme into the middle of a word to change its meaning, tmesis involves adding a morpheme with semantic significance of its own (i.e. a word).