What should I do with this notice?

[Greg]

So I got an electronic notice (on my browser) from my internet provider saying I was violating their copyright infringement policy by downloading shows for free. I called my provider and all he said was to stop downloading these files, uninstall the sharing program and delete all the contents you have downloaded before. After our conversation, I went and uninstalled my file sharing program. Also I did a little research and found there was a program implemented (started this July from what I've read) by major providers that they're cracking down on copyright infringement. My question is:

Will my provider know if I deleted the contents I've downloaded in the past?

There are some shows I want to keep because I like to watch some shows over and over again. IMO, the only way they'll know that I still have the files saved on my computer is if they hack into my computer (which is an invasion of privacy). Don't get me wrong. I am definitely stopping the file sharing but I want to keep some shows.

Also, what's considered copyright infringement? File sharing is a no brainer. However, if I go on youtube or some other site where users can upload vids onto their site for viewers to look at, is that infringement also? Last thing I want is to have another notice on my screen stating I'm violating their infringement policy again.

Thanks