Carol, I would be cautious with getting the bleach on the ornate tile. It won't hurt the grout, but that might be difficult to treat the grout and not the tile. If you need to refresh your grout, consider a grout pen which should be much easier to control.
I don't know the tile but it is usually glazed so I don't see why not. I'd test it though. Lots of time I just pour bleach or spray with Tilex to really clean. Rinse well and seal when clean. Let dry overnight before sealing
I've used it on my shower grout, but at 50% strength. Meaning, I diluted the bleach with 50% water.
I can’t find the brand name of your tiles.
If they are marble, marble is very soft and chemically etches quite easily.
I would not use chlorine bleach on any grout, because it is hard to rinse off.
I would use an old toothbrush with the neck bent so the head is perpendicular and very mild soapy water.
In the long term, I would dye the grout a dark color.