We were there in the afternoon and did not see anyone jogging but that was almost a year ago. I believe you can get an email address for the stadium and perhaps could contact them directly. There is also a tourist information center in Athens which does have a website with a contact form that you can use to ask questions.

Sorry for late answer. I think that your trip is over. About this I think that it is up to you what you choose after jogging if your trip has not passed. If passed, sorry for very late answer. Happy travel! :)

March - October: every day between 8am and 7pm. November - February: every day between 8am and 5pm

You can probably visit quickly in about 20 mins if you don't care to do the free audio tour

I don’t know the amount of the entry fee, but you can view the stadium without going inside. There’s not much added viewing by going inside.

would agree 40 minutes but take a little extra time to see the temple of Zeus which is just a few hundred yards from the arch of Hadrian on the right as you walk towards the stadium

If I recall correctly, the handheld audioguide tour (which is included with entry fee) takes approx 45 mins to talk you through the various stations around the stadium. My 18yr old daughter and I visited in mid-Dec 2018 and enjoyed it more than we expected. I was glad we took the time to pay the money to visit, rather than just look from the front entrance area.

Unfortunately we didn't attend an event there. There should be a seating chart to help you make a selection.

Yes you can, I just did and felt surreal 😉

Yes there is a park nearby. Not the nicest area of the city but I didn’t feel it was dangerous