What do you make your tenants agree to in order to protect yourself and your property?

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I am concerned about my liability in my rental real estate venture. For instance, my insurance will not cover pets, so I want to make sure my tenants agree to not keep dogs. Am I legally protected if I write up a list of rules and make each tenant sign the paper? Is it better to have an attorney draft a more professional statement?

Finally, do you think the list of statements below is sufficient to protect my liability? Is there anything else you would require if you were the owner of the property?

1) Tenants cannot keep any pets.
2) Tenants can't sublease their apartments without approval from the owner
3) Tenants must keep all smoke alarms, carbon monoxide alarms and fire extinguishers in working order
Additional information
4) Tenants must keep renters insurance to protect their property.
5) No tenant can live in the home that has been convicted of a felony in the last 5 years (contigency of my insurance)
6) Tenants are not allowed to seal windows shut
7) Tenants are not allowed to block access to property from emergency or fire personnel.
8) No tenant can be an elected official or member of a professional sports team ( a contigency to my insurance- seems strange to me!)