Insurance: what is public liability and completion insurance?

All of the insurance questions depend on the jurisdiction you are in. Insurance varies widely from country to country and in subtle, but sometimes significant ways, from state to state. My guess on public liability insurance would be coverage for claims of injury to the public at large as opposed to your client. A term I am more familiar with is general commercial liability insurance, which covers all sorts of things for a business from trips and falls on the business property, to employee theft, to reputation injuries. You have to read the policy to see the actual coverages and exclusions.

I have not dealt with completion insurance, but my guess is that it provides coverage for claims of injury to your client if you do not complete your work on time. I would be very careful about this type of insurance and read the coverages and exclusions very carefully to make sure it covers what you want and need. I would not think that most web designers would need this coverage as the damages for a late web design would be very speculative..

Copyright is a whole different subject. There are different copyright rules from country to country, but the United States governs copyright at the federal level, so there is no difference from state to state. All material is copyritten unless it is in the public domain (even this answer). The copyright symbol is not required, but does provide more protection. There is a fair use doctrine and other doctrines that allow use of protected material. This is a very complex area of law that requires years of study to really understand the nuances, and then lawyers specialize in areas of copyright like web issues, print, art, etc.

I intend to handle copyright issues by using open source products or products that are free. Always include the copyright information that came with the product or cite the source of the code. Code is tricky because there are only so many commands. The protection comes in a compilation of code to create something special. For example, the css code: h1 {color: blue;} itself does not have a copyright. But if that is coded into a product like Bootstrap, it does have a copyright in the context of the larger code compilation.

If you look to another code for how to solve a problem and then you use the concept in your own work, no problem. If you copy one standard code block, no problem. If there is a particularly innovative code block, you are getting closer to having problems. If you copy functionality, you may be in more trouble. Copy all of Bootstrap and pass it off as your own work, you have certainly crossed the copyright line.