Why your iTunes converted video has no sound?

Because iTunes cannot convert muxed video (the audio and video of a muxed video file are on the same track), muxed video converted by iTunes will lose sound. You can learn more about this issue from apple’s official document, If you come across this problem, you can use Aneesoft Video Converter, it is freeware and deal with muxed video with no problem.

How to hack iPod to play games and music video?

This part is mainly for the old version iPod, coz the new series of iPods can directly play video and game and you don’t need to hack them. If you want to hack your iPod to play Doom 3, you have to install iPod Linux on your iPod, here is iPod Linux official installation guide http://ipodlinux.org/Installation_from_Windows
Or you can take a look at this guide, which I think is more intuitional: http://www.youtubetoipod.biz/guide/ipod-linux-on-ipod-nano-play-music-video.html
Note: It can be pretty complicated to install iPod Linux on iPod, so give it a serious consideration before you do that.

How to manage two iPods on one computer or transfer music between iPods?

Manage more than one iPod on the same computer

Method1
Create multi accounts on one computer, one account for each person to login OS and sync his/her iPod with iTunes.

Method2
Set your iPod to “Manually manage music and video”, and then create a new iTunes playlist for each iPod that contains all the music that you want to send to that particular iPod.

Transfer music between iPods

Method1
As for transferring music between different iPods, you need a special application to do that, I have tried a program named iPod2iPod, it can successfully transfer my friend’s iPod music to my iPod, and here is a guide about it: http://www.top5soft.com/tutorial/how-to-transfer-music-between-iPods.html

Method2
You can transfer music from iPod to your computer, and then re-add it to your iTunes library and sync it to your iPod.