The thing is it's not important enough an event to use this "is that true?" with. It sounds like you're interrogating someone, or something a parent would say to a child, then if you say "this park" it means you are both in the same park so you wouldn't need to use "I hear.." logically you would say "I've never seen you here before," or "I think I've seen you here a few times," or something like that, and I thnk "I hear.." is an odd phrase to use with ordinary daily events/actions. I'd say you would normally use it with one-off, interesting events, like, "I hear you're leaving!"/"I hear you've got a new job!"/"I heard you've got another kid on the way!"
In terms of the grammar, I would definitely go for the first option. "I'm running in the park every morning" sounds wrong to me.