I have made Business Rule for CRM and activated it, but it doesn't perform any action it should. It is activated, by the way.
I have checked the conditions multiple times and the look fine. I have also made JS Web Resource with the same conditions and it works.
The entity I am working with is custom entity(not activity). Is there anything I should enable on my entity to enable business rule, something like: Business Process Flows, Activities, Connections etc. or should I look for problem solver somewhere else?
When Business Rules have issues, they simply don't run (no errors, no nothing).
Make sure the scope of the Business Rule is correct (if you're not sure, pick the all forms option and safely forget about it).
Also, all the fields appearing in the business rule must be placed in the form body, if even only one is missing then the rule will not run. They can be locked and/or invisible if that's an issue.
Business rules that will be applied to Main and Quick Create forms, and to an entity, in the Web application and Microsoft Dynamics CRM for tablets. It is applied to the Main and Quick forms in the Outlook client in online and offline modes. (https://technet.microsoft.com/en-us/library/dn531086.aspx)
If all is good and the rule still doesn't run, clear it out then test it after each single change you make.