The phone is most likely locked with a passcode. If that's the case, I would expect you to see a number entry keypad with "Enter Passcode" above it and the lower left key should say Emergency Call. If the message above the keypad is Emergency Call, then the lower left key will be a back arrow. Clicking the back arrow will take you to the Enter Passcode screen. The only way around this would be to factory reset the phone.
The icon on the doc is just a link to the actual application. The link is broken which means iPhoto has either been removed or, more likely, deleted. Open up the Finder and go to the Applications folder and see if it is there. If not, you're best bet is to reinstall it with the CD's that came with the computer. If memory serves, that model shipped with 2 CD's - one with OS X and the 2nd with iLife applications, including iPhoto.
The iPod Touch 2nd Generation cannot be updated without a computer. Apple didn't release that feature until iOS 5, which isn't supported on the iPod Touch 2nd Generation. You're devices supports up to iOS 4.2.1.
Sorry, but you're dad's right this time. Apple discontinued support for the 3G whit the release of iOS 4.3. That was in 2011 when the 3G was already 3 years old and had been discontinued. The 3G just doesn't have the processing power to run the games that require iOS 4.3 or above.