Hello.
Can notification be sent by email in the advanced plan?
Can push notification be sent to a shared device?
Email notification is possible, but beware, there is a limit of 1000 emails, maybe for a year 
That is very little.
I have 2 other homes shared as a member (more is also not possible, there is only one admin) and I receive push messages from devices from one home (only from devices, notifications from scenes also nothing), but nothing at all from the other home. If I had only a certain device shared and not the whole home, nothing came either.
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1,000 emails/36.5day
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So this is very strange, sometime between July and October 20th, when I received the last email, I got to 1000 emails and since then not a single one has come.