Okay first - Lyrics: Go to the song you want to add the lyrics to, right click and select "Get Info" then go to the "Lyrics" tab and type or paste the lyrics to the song.
- To view them while listening, when you're listening to a song and looking at the album art of the song playing, just tap the screen (so the little bar comes down that has how far along it is in the song, and the three buttons for repeat, Genius, and Shuffle show), and the lyrics should pop up.
Hours: My iTouch lasts a longgg time (a few days) - but only because I keep the brightness on low (Go, on your iTouch - Settings > Brightness, and slide it to the left to what you can stand - me, I can stand it all the way down, and turn auto brightness off if it already isn't) and I rarely ever use it listening to the speakers, those two things really kill the battery. So use the headphones more often, or just deal with charging it every day.
Internet: No, there's no other way you can connect to the internet other than WiFi - your iTouch doesn't have any place to attach the phone jack and other cables needed. Think of it as a laptop - if you had to plug it into your wall, what's the point?
VPN: I'm not really sure about this, however I Googled it, and it came to a Y!A question, and I think this would be helpful - https://answersrip.com/question/index?qid=20080121055417AAzBT6K
Hope this helped! :)