Many sites with sensitive information (such as banks, brokerages, etc) are coded to prevent saving login information. This is for your protection to prevent unauthorized access to your account.

What you're looking for is called a download manager. Some servers just don't support resuming downloads if I remember correctly; however, some of the newer download managers may have found a way around this by now.

It's important to note that the various browsers use different rendering engines, and therefore may display minor differences in your website.