Why did you order anti-virus software for a Mac? There is no such thing as a Mac virus. Are you able to return the software? If so then I would highly recommend it. Not only that, but Norton is notorious for slowing systems down tremendously.
If you absolutely must have anti virus software on your computer (which really is basically useless) then there are free version that would be much better than Norton.
If you are sold on Norton then it should tell you as you are installing it if you need to remove the old version first.
As far as your passwords, there is a Mac only program which is amazing for passwords. It is called 1password
and you can download it and try it for free to see if it will work for you. You will never again have to remember a PW.