Hello, I got a few explanations for you.
Starting with your latest post, NUMBER OF THREADS WRITING TO DATABASE is a number of concurrent threads that are writing events to the database. The default value should be optimal, it can be tweaked to achieve better performance of saving events, but let's say it's more 'advanced' setting.
Reducing events and detections storing time will allow you to save some disk space, especially events storing time.
Unchecking storing filesystem events will stop recording of all file related events like write to file, file opened, etc. They will still be analyzed and exposed to rule engine that is triggering detections, but they won't be stored in a database.
Looking on screenshots that you provided, there is no abnormal situation with EIServer's work, everything looks fine.
Going back to your initial question, I see that you were asking about BIN files growing in size. These are files for MySQL's binary log mechanism (https://dev.mysql.com/doc/internals/en/binary-log-overview.html) which is used mostly for replication. It is not managed by EI in any way. EI is invoking a lot of operations on a database, and all history goes to that log, so it's growing fast, but actually it has nothing in common with EI database size. If you want to check storage used just by EI database, you can check size of enterpriseinspectordb directory size in MySQL's Data directory. So the question is, if you are using replication, and if you need that binary log enabled at all. If not, it can be disabled, otherwise it can be purged periodically.