The website at https://www.wgcpas.com/irs-provides-a-safe-harbor-test-for-section-199a-and-rental-real-estate/ does a pretty good job of putting it into plain english us common folk can understand. 

Does time spent on Accounting and on activities required by the business structure (e.g., LLC membership meetings, reports, etc.) count towards the 250 hours?

No. The 250 hours of rental services are performed during the year with respect to the enterprise. Membership meetings, reports, etc. are not "rental services with respect to the enterprise" since they are of no benefit to the tenant. Excluded from rental services are financial or investment management activities, planning, managing, or constructing long-term capital improvements, or hours spent traveling to and from the real estate.

Does each activity need to be logged with beginning time and ending time or is it sufficient to report hours worked on each day on each type of activity?

The taxpayer maintains records, including time reports and logs, to support the hours, dates, description and provider of the services performed. Understand that this does not mean that "you" personally have to perform the service. For example, if you pay your A/C guy to come out and service the A/C and it takes them three hours, that's 3 hours that "YOU" provided because you paid your A/C guy to perform and provide that service.

In a rental business aggregated of several Schedule E Properties, does the log need to identify the specific property each activity was conducted for?

You actually get to chose. But once a selection is made (with limitations) you can't change it year to year.  The primary limit is that you can't combine residential rental and commercial rental as a single aggregate entity. One reason is because commercial rental and residential rental have different depreciation schedules under MACRS.