Hello and welcome @fuzzmunky 
Trust Levels do indeed have an effect on the different features, functions, and abilities of users. You can get a general overview in Trust Level Permissions Table (inc Moderator Roles)
As a moderator you should also be immune to rate limits (Understanding user statuses, roles, and permissions). Could you describe when you hit the consecutive posts limit in a little more detail? How are you flagging these spam posts?