Firstly, having too many desktop shortcuts is inefficient, as most are accessible from your start button if you are careful. I have not been a fan of other browsers, so have stuck with IE(now)10. I have noticed an advisory from gmail that notes I am not using Chrome and recommends the change. Firefox is used in the local tourist office, but each has its own peculiarities. It is largely due to how cookies are managed by each of the browsers. As far as emails are concerned, I have configured Outlook to deal with all my email accounts, that downloads all the mails from the servers from Orange.fr and gmail.com, and write rules for their arrival in Outlook.
However I notice that if I check mail on the mail.orange.fr server and then refresh the page, I get a warning that cookies are not enabled, and the only way I can get back to the page is to reselect it from my favourites. And that's in IE. so it is not a unique problem. Go back to IE if you can is my advice.