I am under the impression that the adcoms receive the sample as well. However, I understand that anything above 4 is considered just peachy. You don't want to bomb the AWA, though, since it may raise a red flag if your essays are stellar. This is because they might believe that you've enlisted the help of someone else to do your job (i.e. admissions consultant who didn't edit your essays, but actually wrote them from scratch).

You might want to spend that half a day to just read a few samples and pointers from any general book at handy or from this forum. You don't want to be caught off guard right in the beginning, since it may affect your stamina/morale.

Yes, schools do see the writing sample. Whether they actually look at it is another story, however.

Generally speaking, the above advice is correct; a score of 4.0 or above should be fine for most people. That's not a huge hurdle, especially if you're a native English speaker, since a 4.0 is only something like 35th percentile (I forget the exact number, but it's around there). You might want to put in a little extra effort if you're not a native speaker, just to prove to the ad comms that you can communicate in English.

In my opinion, half a day is plenty of prep for the AWA. The main thing you have to look out for is the different approaches to the two essays. Have a look at the templates provided with your prep guide, write a couple practice essays, and you should be good to go.

Good luck!