When I opened the eM Client, it tried to connect to hacked Korean website topstick.co.kr. What’s this all about? I had NOT opened any emails, only the client. 
The only time eM Client connects to a 3rd party website is to acquire avatars. You can turn this off at menu/tools/settings/contacts/general and uncheck “Download avatars from external sources”.
Then see if a connection is attempted again.
Can I assume you downloaded eM Client from the actual website emclient.com?
I’ve gone back to thunderbird. When eM Client goes open source, let me know.