I have been working on ecommerce site and my projects were exactly same with your tasks.
- click event issue: might be actually fired twice and, hence, it looks like not fired at all. (some browsers fire the event twice by clicking.) For more detail, I need to look at the codes.
- payment options: I have experience implementing PayPal and Amazon payment API with customized options in php based website.
- hash password: would use crypt() for secure season.
Please contact me and I will get your project done very quickly.