I don't use wifi, but for Chrome:
You may be able to set up chrome how you want using chrome settings. To do this click on the spanner near the top right.
If you can't do it using that method, you may include
home/tc/.config/chromium
in /opt/.xfiletool.lst
or just some subdirectories of home/tc/.config/chromium.
Not knowing how you are going to use the kiosk, there are many other things which could be suggested.
1. You could install more than one browser, so the user has a choice. That is also install Firefox, and maybe others. It is not necessary, just an idea.
2. If you have Tinycore installed on a hard drive, I suggest using persistent home and opt, and not using backup. This results in quicker start up and shut down.
3. Check out these pages
http://wiki.tinycorelinux.net/wiki:kioskhttp://wiki.tinycorelinux.net/wiki:menuThis enables you to remove things from the menu and wbar, so the user cannot access other things on the computer. You can change this when you want to perform maintenance.
Just ideas, it is up to you.