There are a few things that may be going on; if your Mac uses an older system that hasn't seen update/upgrades
to email application, or in web browser application, that could be an issue behind both of these. ~ They're older.
If your Mac is running El Capitan 10.11.6, the Safari version hasn't seen any security updates in a few years. Also
the Apple Mail may be suspect. Since my El Capitan 10.11.6 has neither of these in use, the workarounds can
be to use Thunderbird email client, and Firefox web browser. (Or any other presently updated third-party opts.)
Since you've not heard back from others in this thread, this was only an option; unless you need to feel secure
and then upgrade the system, if possible, to High Sierra macOS 10.13.6, or Mojave 10.14.6. Your 'mail' may be OK
while old Safari has some issues; banks and other fiscal sites haven't liked that Safari version in awhile.
High Sierra sees some security still. (Mojave is newer.)
Your iMac may be nearer end-of-road in upgrade path.
Can you make the internet applications use HTTPS://?
Good luck & happy trails!🌞🌎