General site analysis and bug report

General information for the website: Bespoke Ecommerce site selling diy products
Description of requirements/features: We want a report to follow some investigative testing work on browser types – IE, Firefox, Chrome, Safari to replicate the problems customers are experiencing with getting products into the basket, logging in and proceeding to a payment address page from the cart. As the site uses lots of Javascript we need to ensure this is working properly and if any back up is present/failing. A report is needed that highlights how the problems are developed at user level and what we need to do to overcome these problems. A general overview of the coding problems from a html validator tool would be useful to get some background assessment on the general condition of the site.
Extra services needed: Customization
Extra notes: Website is bespoke and 3 and a half years old and runs on a dedicated server - Linux Apache. Over the past month we have been continually running into a range of problems being reported by customers which we think might be related to sessions or cookie information dropping at https. We have not been able to replicate any issues at this end. Problems reported consistently as:
• Moving from http to https – login, address payment. Page not displayed at Proceed To Payment in Cart, customers can’t login to their account.
• Buy now buttons go to empty cart – information not being carried across.
• Proceed to payment – Page cannot be displayed.
• Post Code Finder button – error message (3rd party connection) – Object Error on mobile site.
• Site pictures ‘dancing’ around the page.
• Flickering cursor when in basket changing quantity.
• Buy Now buttons not showing on page.