Hi – some great questions there!
When I test things out with our latest release this is what I see:
- The schedule info for an event taking place on a single day looks a bit like August 18 @ 5:45 am – 9:45 am (so that seems to match what you have requested)
- For an all-day event it simply provides something like July 4 (again that seems to match your requirements here)
- …or, if it is an ongoing event – ie, the end date/time match the start time exactly – I see something like July 4 @ 8:00 am (again this sounds like it would meet your needs)
I’m unsure why you are experiencing anything other than this, but I do note that you have a fairly stylized calendar (I’m guessing at the minimum you have some custom templates in place and/or some custom logic somewhere) and wonder if those customizations could be the source of this?
Can you check in with the theme vendor, or try to confirm if this might be the case by restoring a default, unmodified theme such as Twenty Thirteen?