You can monitor Exchange Server health with the native method.
Step 1 - Monitor Server Availability and the Status of Exchange Services
Step 2 - Monitor SMTP performance, CPU and Memory usage on an Exchange Server
Step 3 - Track the Message Queue
Also, remove the external DNS from the exchange. If it uses this as DNS when trying to resolve internal clients, it may fail. It might happen because Google DNS servers know nothing about your internal network. Your internal systems should point to internal DNS only.
I hope this will help you.
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