That's what realtors call charm.
But seriously that looks like just settling over the years. I have a fireplace that has the exact same tile for the heart and it has settled and looks pretty much just like your fireplace.
It's hard to say if there's any structural issues without looking at the floor joist below to see if they are cracked or overstressed, but again this looks pretty typical for the age of your home. I would do the floor repairs on the oak.
It looks to me like you could do two things when you install the heart. One you could chip away the cement closest to the firebox and install the new heart flush with the old flooring and it would make it look straighter probably not level. Two you can install the heart where the edge comes above the oak floor about a half inch to three quarters. They make something called a heart strip that is made for this transition.
Picture of hearth strip (it lays flat not straight up like the picture shows)