I'm pretty sure that you could use that visa to enter Thailand between June 1 and ~ August 30. You would be stamped in for 90 days after that first date of entry, so in your example: getting stamped in on July 25 would yield a date of ~ October 23. Any re-entry permit(s) would preserve this October 23 date.

You may be able to extend this by 7 days inside the country for a fee.

You can convert this visa to other types (work, marriage, retirement) inside the country.

Give yourself some extra time at the airport to apply for the re-entry permit, at least for the first time.