Re: Kostya, I ve been on Nougat since December and the issue started about 10 days ago.
I'm not aware of any changes in push mail recently.
Even with just three folders, if the app's network connections are getting aborted (too much), then you could run into this limit. That's all I can say right now "in theory".
Re: Any progress with canned responses
Aqua Mail has had canned responses for a few years, on the compose screen, Menu -> Quick responses.
Re: also still missing the widget with ability to select more folders and more accounts like in Profimail Go
Not sure about showing Sent (or Drafts or Deleted) in a widget, not a common request for sure.
Re: Star a message from the widget
Google recommends only using one "action" for "list widgets", trying to add more may overload "the system" (too many PendingIntent's inside Android code).