When I try to set rules for an Exchange Web Services account, this option is not there, and I’m not getting notifications from such rules.
Is this by design? And why?
That is because you are creating a server Rule. When a Rule runs on a server there is no one to notify. Kinda like a tree falling in the woods, and no one around to hear it. 
The skip notification option is for local Rules only. So Rules that run only when you have eM Client up and running on your device. You will see a drop-down option next to the New Rule button, where you can select server or local Rules.
So if I want all the same rules to work and have notifications from them, I must re-create them all but in Local Rules mode?
If yes, that would mean these rules must be duplicated? Or else, if they are local only, the changes will not happen on server and will not be synced to other devices, right?
What’s the easiest way to enable notifications for all messages regardless of the rules? Can I set up one local rule like “If I receive a message in any folder, display a notification before any rule kicks in”?