Don't feel bad about not knowing anything about these electronic devices, if you don't you use them you would have no reason to know anything about them. Let me start by addressing the question at hand of playing games. The version that you have selected, the nano, does not have any games available for it. This version of an ipod would not work for what you need.
That being said, the version that you would need will need to have these things in its description or even title, "TOUCH." This means it'd be for a version of ipod that you operate by touching the screen the same as you would with a smart phone. Also, you would need one that is any of the following Generations. 2nd, 3rd, 4th, 5th, or 7th. The best way to look at these is like cars. Each year the newest model will come out and it just improves on the previous years model. For an Ipod, what that generally means is more storage space on the device and they tend to get smaller and sleeker. These devices do not come with the games. To actually get games on the device, you will need to download from the itunes store online. Remember you do not want a Nano, and it has to be a "touch" version of the generations that we mentioned. We hope this helps and please feel free to ask any other questions!
You can use your own music but you have to use iTunes app. You can import CDs, add songs . you don't have to buy music from iTunes to put on there. Just drag your songs to iTunes or rip CD then import to device
No not at all. That's because they don't lock it. All you have to do is click the top button once after you select what you want and the screen will shut off. The music still plays but it won't get messed with in your pocket. If you hold the button down it'll shut it off completely.
Short Answer: Yes, 720p
H.264 video: 720 by 576 pixels, 30 frames per second; Baseline, Main, and High-Profile level 3.0 with AAC-LC audio up to 256 Kbps; 48kHz; stereo audio in .m4v, .mp4, and .mov file formats
MPEG-4 video: up to 2.5 Mbps, 720 by 576 pixels, 30 frames per second; Simple Profile with AAC-LC audio up to 256 Kbps; 48kHz; stereo audio in .m4v, .mp4, and .mov file formats