If they see that i have downloaded from the net but when they come don't find it in my pc, am i off the hook??

if i delete every illegal stuff with safe deletion method just before i open the door to the police so when they take my pc for examination they don't find anything, can they still procecute me because they saw my ip downloading copyrighted material? If nothing illegal is found on me am i free to go?

The only way for them to "see" it was you is via your IP address. If you change that, it's enough. But yes, if they can't find the files they have no case.

Alternatively, if you encrypt your entire drive and give it an extremely complex pass-code (say by bringing it up to NSA specs, which you can they provide a how-to for every OS free on their website) then they can't even access your data without your say so. Which you don't have to as it falls under the fifth amendment for Americans.

If they can't find it.. they can't prove it.. but they can RETRIEVE deleted data. Safest thing to do... don't do illegal activities on your pc.. use someone elses. LOL just kidding on the last part.

why are you asking this, are the police at your door. DONT DOWNLOAD IF ITS ILLEGAL

There is no way to completely delete things from your hard drive. when you delete something, it just makes it inaccessible, information on your hard drive is in magnetic code, the code is still there somewhere, and can be recovered with the right software. So stay legal unless you want to get caught