It appears that your understanding of the components is a bit off.

1. This can be performed, but is not recommended because you would then miss important error messages like potential kernel panics.
2. This can be done in a kernel configuration.
3. You would have to compile thekernel modules for the specific touchscreens you wish to use into the kernel as installed drivers or modules.
4. The video performance is decided by the included drivers, the GUI used and the configuration of the screen.
5. This seems a bit contradictory due to your following questions.
6. This requires applications for dhcp addressing and wireless configration, so it is not included in the kernel.
7. Again, this is another contradiction because it is not part of the kernel it would have to be added as an application within a full OS.
8. This is another application that would have to be installed within a full OS.
9. This seems to conflict #11, will it need to jump directly into a stndard user account in CLI or a GUI, if a GUI then which one?
10. This application would require a full window manager and the X11 libraries and applications to be installed.
11. So, you want password entry for physical access and remote desktop with authentication also. This seems to conflict #9

What it sounds like is you do not necessarily need a custom kernel, what you need is a customized distribution.

You will need to look further into your specific needs, exactly what hardware should be supported, what cpu architectures, what gui, will you use centralized management, what kind of a firewall should be applied, what shells should be available and what other capabilities should the user have?

If you can answer enough question then we might be able to help guide you to strip down a distro for your needs and package it for re-distribution.

There are distros that do some of the things you want, do a little searching and tinkering. No point in asking to build something the already exists. Remenber this is linux, It is designed for light weight alternatives to other OSs. Like what fillopt said, know exactly what you are trying to do and find a distro that meats your criteria.

Best of luck!!!

Here is what I have to offer for advice.

Drivers:
The network drivers may be a problem because ralink and realtek aren't too good about open distributing linux based drivers. Community based stiros have the greatest problem with this because they have not negotiated licensing deals with those companies to use the drivers and firmware, so you best bet would be to start with a commercial distro like Ubuntu, Fedora, RedHat, Novell SUSE, etc..

User Interface:
To give you the user interface option you wish to get you can run xterm on top of the X window manager and have your custom application set to start on GUI startup. This will present you with your application and a terminal in the background for crash handling. However it may be possible to just have X11 to boot with the application started only, I just haven't tested it.

Keyboard:
You can disable or blacklist the keyboard driver modules, but if network communication is ever lost (such as the network card dying) then the box would be dead without any way to physically access and update it for new hardware. I am also unsure if the keyboard modules would be necessary for remote command to be accepted. I would recommend physically blocking the keyboard and usb ports so they cannot be accessed by the users as a simplified method.

Touch Support:
The kernel and X11 window system have support for various touchscreen interfaces so that shouldn't be very difficult.

Remote Administration:
For this to be safely implemented you will have to consider if the remote access with be GUI or CLI based, then install the necessary services, security mechanisms and firewall logic to keep it secure.

You also must advise whoever will developing this platform of the type of consumers and industry this will be distributed to so they can adjust the access methods and security to best fit the needs and capabilities of the users.

Now for this project I would normally be willing to experiment to see if I can get it working, but without the physical hardware and necessary software I cannot reliably give you any configuration or installation files. Your best bet would be to contact a contract development firm and supply them with the necessary hardware and software for them to build and test your goal platform.