Android - Restricting Web Access to a single domain on Android tablets?

Yes all this is possible but you'll have to root the tablet and whether or not that is possible will depend on the tablet.

Here's the answer to each request:

1. Yes, you have to edit the hosts file for which you'll have to root the device.
2. Yes, any browser (I recommend Dolphin HD) will let you set the home page, so just set this to the page you want it to launch with. With the Launch After Boot app (~$1.60) you can set the browser to launch on start-up.
3. Yes, the aforementioned Dolphin HD Browser has a "Full Screen" mode under settings.
4. Since you are rooting the device you can just uninstall the messaging (SMS/MMS/Email) apps.
5. Yes. This app requires a rooted device (and dropping $2): Boot Animation Changer Pro

All in all this is possible assuming you can root you device, and while it won't be easy, it also wont require you programming any custom solution.

Edit: I should have mentioned that going "Full Screen" on the browser will not prevent people from navigating away from the browser screen to other parts of the device but you can basically uninstall every single app that you don't want your people using, and uninstall the market so they can't install more apps. You can also Password protect apps that you don't want people using with an app like App Protector Pro ($2). Any enterprising person will be able to get around anything you do with some work but that can be said about any workplace restrictions.

Edit #2: Don't quote me on this but I'll bet you could use Tasker to furhter restrict access to the device and/or services. Assuming you guys operate during set business hours and are at one bricks & mortar location, you can set location and time based restrictions so when they are in the store during business hours only certain things are possible. You would just need to password protect Tasker after setting it up.