In the early days of the internet, web browsing and sending emails were two entirely separate things. You used a web browser (usually Internet Explorer in those days) to view web pages and an email client (almost always Outlook or Outlook Express in those days) to send emails. So email links in web pages were designed to open Outlook (or Outlook Express) with the the recipient's email address already filled in. Some websites still have that type of email link but such a link won't work if either:
(a) you've not got an email client (such as Thunderbird) on your computer ; or
(b) your computer hasn't been set up with the correct 'file association' to tell it which program to open when you click on a link.
So you could well be clicking on email links which won't work because you've not got an email client installed and configured on your computer. The solution is to RIGHT-click on the link, select 'copy email address', then paste that into the address bar of a blank email which you create elsewhere.
Right-clicking might also solve you problem with downloading files. (Right-click and then select 'Save link as'). A bit of googling though suggests that the problem might clear itself if you empty Chrome's cache:
https://support.google.com/accounts/answer/32050?co=GENIE.Platform%3DDesktop&hl=en