Key Takeaways:

Can I backup my computer software?
Yes, under certain conditions as provided by section 117 of the Copyright Act. Although the precise term used under section 117 is “archival” copy, not “backup” copy, these terms today are used interchangeably. This privilege extends only to computer programs and not to other types of works.

Section 117 does not allow you to sell backup copies to someone else except when such backup copies are sold together with the original lawfully owned copy.

Can I copyright my website?* See below.
The original authorship appearing on a website may be protected by copyright. This includes writings, artwork, photographs, and other forms of authorship protected by copyright.

Copyright law does not protect domain names.

Is it legal to download works from peer-to-peer networks and if not, what is the penalty for doing so?
Uploading or downloading works protected by copyright without the authority of the copyright owner is an infringement of the copyright owner's exclusive rights of reproduction and/or distribution. Anyone found to have infringed a copyrighted work may be liable for statutory damages up to $30,000 for each work infringed and, if willful infringement is proven by the copyright owner, that amount may be increased up to $150,000 for each work infringed. In addition, an infringer of a work may also be liable for the attorney's fees incurred by the copyright owner to enforce his or her rights.