Yes, they work with anything that has a standard 3.5mm output jack.
Yes, Beats by Dr Dre work on all iPod types
Not at all. Beats may be used on any media player with a 3.5mm headphone jack, which is standard for most devices nowadays.
An iPod Touch would be much better. If you are looking for good headphones, nothing with a celebrity's name on them will bring you quality. Sennheiser is a great brand of headphones to look at.
The difference between iPod headphones or earphones and Dre Beats has to do with style and how the headphones are worn. Typically, iPod headphones are "earbuds" and fit directly in the ear. Dre Beats are worn around or over the ear and have better sound quality. Additionally, Dre Beats tend to resemble retro headphones of past decades. They also block out other sounds.
Yes
YES! any ipod/iphone/ipad is!
Yes, Beats by Dr Dre will work with any device that has Bluetooth.
Yes, Beats by Dr Dre work on all apple products
Yes, all smartphones, iPods, iPhones and iPads work support Beats by Dr Dre.
Beats should wok with every generation of iPod and iPhone
All iPods output music equally so there is no real answer.
Beats by Dr. Dre Wireless are the wireless Beats by Dr. Dre, below is a link to them.