go to settings and into general
iPod Touch: press Settings on the Home Screen>General>Date & Time>Set Date & Time. iPod Nano (scroll wheel): Settings>Time & Date...
go to settings/general/date & time
No you do not have to pay to access the Internet on an iPod touch.
in settings
It depends on what you mean by 'filter protect'. There are restriction settings on the iPod Touch (which requires a 4-digit pin), which can prevent access to Safari, iTunes, not allow App Store purchases, and so forth. They are available in the settings (the title will be Restrictions). That is about as close as you can get to filtering certain things on an iPod Touch.
Yes, you can access your email on the iPod touch.
Check the date. It must be correct.
If you can't access apps on the iPod Touch, then you should try updating the software version of your iPod Touch to the latest version.
You cannot delete the legal information in the settings on your iPod Touch.
No. The only requirement for internet access with an iPod Touch is access to a Wi-Fi network.
Yes, but only via Wifi ! You have to connect your iPod Touch to a wifi network, via the Settings of the iPod
You can get lyrics online with your iPod touch but only if you have Wifi.