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Sorry, But No
No, there is no way to jailbreak iOS 6 without a computer. Only older iOSes can.
No. If you are running 3.1.3 (the latest firmware) on any iPhone, then you can jailbreak without unlocking. If you are on a firmware below 3.0, I think you can jailbreak without unlocking. I would like to add that I am pretty sure jailbreaking an iPhone is illegal because of your contract with Apple. Find me on YouTube: TheJailbreakGenius
you can jailbreak any software
No. Your jailbreak will remain as it is. Syncing your iPod does not alter the jailbreak in any way.
Music-wise, jailbreaking does not get you any free music that you wouldnt have had without jailbreaking it. You can find free music anywhere online, with or without a jailbreak. Jailbreaking does not get you free music, but does get you mods, apps, etc.
There is no requirement to jailbreak your ipod, in fact it will invalidate any warranty you have.
HDMI splitter is compatible with Digital Audio. HDMI cables and splitters are carrying audio and video signals without any data loss or downgrading quality.
Yes. Simply restore iTunes without clicking any options or anything and it should be back to normal.
You can jailbreak ANY ipod or iphone on ANY firmware by using a software called ''Spirit'' google it and check thats how i jailbroke mine lol sorry to say this but..... it cant jailbreak iOS 4.0 but it could jailbreak anything under 4.0
Yes with jailbreak
No, you cant. You can only jailbreak I-Pod Touch and I-Phone and I-Pod Nano 1st generation!