1) I accidentally used my Music Box, therefor making it crumble. Can I get another one?

2) Will you be alerted if Mew is on the floor you're on?

3) Will Mew always be by the exit or where you start on the random floor it's on?

4) Will Mew's floor be smaller, like the Regi's?

1. Yes. Go through the Regis again. Before you ask, even if you recruit one the part will be there by its lonesome (not if you bring the Music Box or relevant part, however).
2. Look for "Mew used Transform" in the text box thinger. Other than that, no.
3. It will be anywhere on the floor, but it will only be there when you start a floor. (No kill 100 Pokemon and then it magically appears on the floor or something)
4. No. It's just a regular floor.

Strange I know all this, yet I haven't even met Mew once, eh?

-Gardevoir~

you just have to be patient for the regis. it will involve several trips possibly. it took me about 6 all up. i had a friend bow and my pokemon was level 100. just be careful. when i caught i used an escape orb, only to discover that you cant use them on boss floors. it said "a mysterious force prevented the orb from working" or something like that, and the orb disappeared. i had to go all the way to the end. on the other hand, when i caught , it instantly ended the expedition, which was annoying because i was just about to open a door with a key when i caught sight of mew - so i went and battled it and it joined me, and i didnt get to open the door.

Won't mew use Transform on your first few steps? So that you could know that mew is there before you reached the door?

Just because the Mew knows Transform doesn't mean it has to use it. in the two times that I have encountered Mew, one time it Transformed into a Golem, iirc (and I "hunted" it down). The other, it was in a Monster House, non-Transformed. Unlcukily, it hasn't joined me yet...and I do have it's Friend Area, Final Island...

mew was asleep when i caught it. so it had no chance of using transform. (or any other move for that matter.) i wouldnt rely on looking for transform to test if mew is on your floor. use the x-ray specs and at the start of every level make a mental note of how many pokemon are there, where they are etc, and make sure you kill 'em all!!!!!
especially

I don't understand what you just said, so can you say it again, being more specific?

well for ur answer the room will be the same size as any other fllor, u find him in buried relic, i found him on floor 45, and no u wont be alerted, itll say that mew has transformed, if u use ur music box wat i did wat i ended up dieing so i got it again. When i found mew he had transformed into a electrabuzz so lol. But i had articuno on me so i didnt get him...

i still havent got mew and i went through the buried relic twice
but i still got regirock

You don't need Final island to go to Buried relic, Titan_of_lightning

okay, you need final island to recruit mew, but not buried relic

and I have not tried my luck on mew...