What do blood tests for inflammatory markers in look for? Can they detect all or some cancers?

Limited usefulness. Labs like c-reactive protein are markers for what some physician describe as "generalized inflammation" which includes both patients seriously sick with classic inflammatory disease and people who are fat / out of shape / or are perhaps independent risk factors for atherosclerosis. They're not useful screens for cancer.
Inflammation. Blood tests like CRP and sed rates among others look for inflammation. Most all of them are not specific to one or more kinds of inflammation. If positive it gives physicians a key to look deeper to see the cause. A lot in that department depends on a good history from the patient and a physical exam.