What are the rules regarding charging a broker fee or a policy fee?

Do I charge surplus line tax, fire marshal tax and/or stamping fee against the broker fee/policy fee?

No. Surplus line tax, fire marshal tax and stamping fees are only assessed against actual premium.

Are there restrictions or rules about how much I can charge? Are there rules about what records I must keep relating to the fees charged?

Yes. See paragraph (e) of Section 500-80 of the producer section of the Illinois Insurance Code.