I'm in town for business a lot but have to run super early to get my miles in (5am local time). Can I go to this new running center / trail at that time in the morning? It's only 7 miles from my hotel.

pair up

If there's no one around I'd wait till there are at least a few people tjat you can see.

Yes, this is a city park

Yes

Absolutely

The trail doesn't close as far as I'm aware. I haven't been at 5am, but by 5.45 its quite busy, so you're unlikely to be on your own. You're probably best to park by the tennis courts though.

Yes you can