So, how about friendship evolves? Do i have to max out my stats with a given 'mon in Pokemonamie? (in this case, Azurill, who is growing rapidly as a baby despite showing no signs of evolving. I don't think i've ever raised a happiness Pokemon before, ever) Or is it similar to the old one of "use them a lot and don't let them get status ailments"?

No more moves

Get him to 51 to learn Sacred Sword, then use the dusk stone

Then go to the move relearner to get him King's Shield

Friendship is different from Pokemon Amie. As from now, only one pokemon evolves from max. affection on Amie, which is Eevee -> Sylveon.
Friendship is measured in times your pokemon won battles, how many times you used items on him, how many steps you took with that pokemon as your front pokemon, massages and so on. The complete table is as follows (unless there was some change this gen):



The values after the slashes are if your poke is captured on a Luxury Ball. Also, making the poke hold a Soothe Bell will increase the positive values by x1.5.
To evolve with friendship, your poke needs to hit the >220 Friendship mark.

@_crazy_man - Thanks man, i'll hold up the evo for now. Where's the move relearner located at?,

In a house in Dendemille Town, move deleteer is also there.  They were a old couple. 

Thanks, I haven't reach that town yet, i'll keep an eye out for both .

New pokemon and mega evolutions stats are up on Serebii. Mewtwo x/y have 780 total base stats wow.

Mewtwo X/Y is literally more powerful than God (Arceus)

By a fair margin too. Garchomp and Tyranitar are god level with 700 BST!

Sadly Mega Chomp is anything but godlike. Reducing it's Base Speed to 92 and increasing it's SpA to 120 is nothing short of ridiculous. 

Had no idea they reduced its speed. They have to keep him balanced somehow I guess.