How can I tell boost cron run to delete a file If I have a custom module that maybe adds some fields, or reorders some data which is to be shown in the frontend: How do I tell boost, that the cached files should be deleted on the next cron run after I've made some changes?
First you need to set a flag which indicates that new fields are added. Can be a variable_set() or something similar thats stores values in DB whenever new fields are added.

In your hook_cron() you should check if the flag is set or not. If set clear Boost cache using boost_cache_clear_all(). Unset the flag once cache is cleared.