After starting the eM client following window appears:
After ignoring all and closing the window everything works OK. Where can be the problem and how to solve it?
Starting eM client with repair switch or change task settings in navigation options does not help.
This can happen if you eg: don’t have any Google tasks or if the current eM Client Google tasks have got out of sync with your online tasks.
So first if you don’t have any tasks, create a task. Then close and reopen eM Client.
Next if you already have current tasks, then try running the repair on eM Client Google tasks as @Gary advised in the following thread post.
Yes, I read @Gary’s advice and I did it. Did not help. I tried it once more, always the same 
As repairing the Tasks didn’t work, then if you have been making regular backups of eM Client, click “Menu / File / Restore” and choose a recent dated backup when you know the tasks were working. eM Client will then sync all new mail, calendar and tasks etc when it next connects.
Now if you haven’t been backing up eM Client or the restore didn’t work, then you could try either removing all your current tasks and readding them and see if that fixes the problem, or failing that, you would have to remove and readd your Google account using the automatic account wizard via “Menu / Accounts” & setup as new.
Lastly if removing and readding the account still didn’t fix it, then you might need to update your current eM Client version depending on how recent it is. You can see and download all the various versions from the release history page.
Note: Once you do get the tasks working, create a backup via “Menu / Backup” to save that setup.