Have you filled in all the settings correctly? 

We did everything as described: Google Project ID, Google Project API Key,
Onesignal app ID, Onesignal subdomin but we can't subscribe.

Isn't it possible to use the plugin as before?

You can use an old version if you want, but this should work. Is your site http or https? 

If it's http then save your settings when all details are entered. You should then see the red bell in the corner. Click this and you should see a pop up (make sure they are not blocked) then allow notifications and click the subscrbe button again. 

I'm using http. When I save the settings there is no red bell. When I click on subscribe button there is no action.

I also checked it on onesignal and I get this message every time:
We haven't detected any subscribed users yet for this platform. Try some of the tips below, or contact us for support.

• Verify that the OneSignal App ID is correct in your app or site.MY APP ID
  
• Run OneSignal.LOGGING = true; before OneSignal.init and check your Developer Tools log for errors or warnings

Could it be a conflict with another plugin? Maybe I'm the only who has this problem. Sorry to take up so much of your time.

If the red bell is not showing then there is a problem with the settings you've entered or how you've set up onesignal. Can you please PM me a screenshot of your settings page? 

Also open the debugging console in your browser and look for any errors there when you load your settings page