Hackers can I believe text you this stuff. They can send you authorization s asking for your password, using exact company logos, and ask for your password from a seemingly safe banner using an address such as this....
www.gmail.com seems very safe to click on, but it may be a false ID, then you click on it, thinking its really gmail, but it's got a hyperlink attached to it. You wind up at another site,-- and now you have virus, and your computer is controlled by some sicko.
The above link is only an example. I was just making a point. Theres no need to click on it.
To my knowledge, none of your typical email providers would explicitly ask for your pass words. If you are getting asked out of the blue for any type of authentication, that would be my first concern.
Using a virtual onscreen keyboard may help a little bit. It just depends on how sophisticated the keylogger that they are using is. However, if there were able to get a keylogger on your system, I would be worried about getting that computer offline and I would just wipe the HD. Nice thing about running Linux and running VMs, it's not that bad to deploy backups to both.
I stopped downloading my emails to my computer years ago. I keep them online, with my own domain email which I use online Roundcube. My other email is Gmail. I like to keep online because I can access all my emails from any online device and computer anywhere. I guess I should get it setup to keep the emails online AS WELL as download them onto my mail computer for backup... Maybe Thunderbird as Old Paint suggested.
IMAP connection (versus a POP3) is what I like to use. Thunderbird does this very well. Which enables me to send, view etc on all of my devices. If I want to download and archive emails, Thunderbird allows for that as well.
MS did a very bad thing in the early years, some of which continues to this day, when they really integrated IE and Outlook Express (although I do miss Outlook Express) throughout the rest of the OS and, especially with Win 98, every user account and the same amount of permission.
Now, they have made changed to the UAC that helps from XP on (ironically most users don't take advantage of that, how many on here only run one account on their computer?), but that full integration of IE still persists for those that use IE on Win 7 and Win 8 (I don't know if it still exists with Edge in Win 10 or not, I would say probably so given MS' history, but I don't know for sure).
No matter what PC OS you use (Linux, Mac and/or Windows) or what email provider you use, quite a bit of the security of that device or whatever online services that you use, really depends on how you do things. What emails you open, what you download, what sites you view and perhaps the biggest thing, how secure are your passwords. Secure in IT terms is quite a bit different then what people think of as secure. At least in my experience.