I am sorry you're confused, but I hope I can help clear things up for you.
When can what types of actions be used?
Unlike some TTRPGs, Case Files doesn’t use defined actions. Players describe what they want to do, and the games master narrates the results. If the outcome of a meaningful action by a character is uncertain or could lead to meaningful consequences, the Game Master (GM) may call for a check. An example of when/how checks might be used can be found in my prewritten case The Union Bleeds Red
What about actions that don't have anything to do with any of the attributes?
All checks are tied to one of the three attributes: Physical, Smarts, or Charm. If it’s not obvious which one to use, pick the one that fits best based on the context.
What if more than one skill is relevant?
Only one skill die is added per check even if multiple skills are relevant.
What is the extent of use cases for each skill?
Skills are intentionally broad. The games master has the final say if a skill applies, but players are encouraged to be creative and justify how a skill might be used.
How does combat work -- when is it initiated, what are the weapon damages and ranges, where is our health stat?
As combat is not the focus of this TTRPG, it is treated like any other check. There are no separate health or damage systems; instead, use narrative consequences. These consequences can come from the Danger system. With games masters using this system to inflict injuries or kill player characters , as well as other complications such as a suspect escaping.
What are our characters' origins -- are we police, private detectives, random people that happen to be good at some things? Do we belong to any organization, or know each other?
The short answer is it's whatever your group wants it to be. If you would like a setting where the players are city-hired detectives, please check out my setting guide here: Veltro City Handbook
Hope this answers your questions