That is impossible without seeing pictures, getting a feel for the layout of your home, and seeing the tile you are considering - How far apart are the cooktop and fireplace? Are the design elements and colors in the room similar? What do the tiles look like? What style is the fireplace surround? We need LOTS more info!

Ditto

Understood but as a general rule?

Is the fireplace in the kitchen? If so, then perhaps so. If the fireplace is elsewhere it might not be necessary or even desirable that the two tiles match.

There is no rule but you need to post pictures if you want help.