To change the number of messages a member can send from admin:
Settings->Membership Levels->Click membership type->Click "send messages"
You can change the number of allowed actions for any of the actions this same way.
No, there is no way to see the outgoing emails from admin. AntonLV has a mod called "scam net" that will let you see and filter emails though.
Having said all that I doubt your account was suspended because of emails sent from the built in message system. It's more likely it was the "matching" emails the site sent automatically.
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