NOTIFICATION IF RENTAL AGREEMENT HAS NOT BEEN SIGNED

If there was a way for the host to be notified if the rental agreement has not been signed by guest, that would be very helpful.

This is already possible - simply set up an email template and trigger as a reminder to yourself:

https://www.ownerrez.com/support/articles/reminder-to-myself

Set it for, say, two days before arrival, with the Criteria of Signed Agreement = No.