As I begin to learn Web Development I want to practice as much as possible and I thought that choosing random websites and trying to code them would be a good way to practice and improve my coding skills. My question is: can I do that and post the code here in Code Review to ask for help?
You might want to look at Do I have to worry about copyright issues for code posted on Stack Overflow?. The websites you're copying are generally going to have copyright notices. They may conflict with the stackexchange.com copyright.