Indeed most of the information can be found in the above articles.
Specifically regarding the above questions:
1. The above situation sounds like an issue encountered in the past and described in sk138033: Hit Count stays at 0 for some rules, please follow the instructions in the SK, if the issue is not resolved, please open a support ticket, so we can assist you.
2. Does the Hit Count for an ACL depends on the logging we enable on the rule? No you don't have to turn on logs on any rule to get hitcount information, the pre-requisite is to make sure Hit Count is enabled. First from File->Global Properties->Hitcount. Afterwords open the relevant gateway object, and make sure Hit Count is enabled in the Hit Count page