@piotrekzielony thank you for your post question and welcome in the UVdesk community.
Looks strange to me you get all email if the ticket is created by email and no email if the ticket is created from the web interface.
Can you check if in the footer operator Dashboard you can see the UVdesk version that should be the 1.0.18? also what version of PHP are you using?
Let's wait a developer reply here. I don't know if the email notification issue is because the ticket has maybe not assigned to a team. Your workflow seems assign the ticket only when the operator reply to the ticket.