Radical Android customization
While I agree with Uwe on #1, it does not correctly relate to your question. What you want is only one visible app, so the users cannot switch to any other. That's what Kiosk Mode is about: Creating a "jail" to keep the user in -- while the "admin" can "break it" for configuration etc. (which would e.g. require a password then). For alternative solutions on "Kiosk Mode", just search our site for "kiosk".

Second, there are a lot of "App Lockers" and "Child Mode" apps available, which are also a variant of Kiosk Mode. Simply search the Playstore for "app-lock" to find a good selection.

For #2 I must disagree with Uwe: Unless you're a developer, you cannot make "every app" a home screen (the app must register as such). But this should be handled by the app providing the Kiosk-Mode -- so watch out that this feature is available with that (keywords would include "autostart", "launcher" or "homescreen").

Not sure about #3. I know there are big touchscreens around, but I have no idea how they can be operated by an Android device. Taking a good guess, "Google TV" could be involved with that ;)