I think this will be fine, generally you can mix florals. If you were to introduce anything else maybe pick up the stripes, birds or butterflies that are in the pattern ( or the stars if you also have the sheets). If you wanted a cheap update add some butterfly vinyl ŵall stickers over the headboard. I'd buy a couple of extra sets whilst there on sale, as she gets older maybe you could then change the walls to either the soft white or duck egg that are in the pattern to give it a different feel with a birdcage pendant for example.

From a practical point of view:- Obviously you can put what you like on top of the hearth, tile straight over tile on tile, but you'd need to make a surround as you'll see the edge. I'd make sure that your hearth tile isn't going to clash or look wishy washy against the white skirting and the marble of the actual fire surround. Also, as I see it's a working fireplace, if you go for something very light on the hearth, the grout will be filthy within days. You also couldn't go for a tile with a porous surface as this would lead to the tiles themselves also getting dirty. You'd either have to seal the surface of the whole hearth to make it cleanable, or go for a shiny surface tile & somehow seal the grout to keep the soot of it. Once on, never off. This is why hearth's are usually grey / black with grey grout. I'd keep the hearth as is, because it matches the fireplace and is a practical colour. With regards the tiles on the fireplace, they are inserted from the back of the fireplace in to a frame not visible from the front. The only option you have without taking the fire out is to tile on top of those tiles. You will then get the same problem with seeing the edges as you would if you tiled the hearth. You can buy thin 'pencil' edges to possible combat the problem such as these from B&Q Pencil Trim you just need to put your tiles in between them. It all depends on what the tile surface is like and where the originals butt up to the cast iron. Maybe you would be better off with fire retardant tile paint for the fireplace tiles.

There will most likely be a gas pipe running under the floorboards to that gas supply. You need a gas engineer to re route that gas pipe slightly so it terminates at the fireplace itself (not sure why it doesn’t already tbh). Hopefully this can be done via a cellar or crawl space rather than lifting the floor, however if boards do need lifting it probably won’t be many. Then you need something like a Nu Flame gas fire (like a black box which sits in the grate) as mentioned above. Nu Flame is a good brand, not the cheapest out there but good quality I’m told. Again gas engineer needs to install this.

We've been through a few fireplace dilemmas over the years. The main thing is that making it in any way usable will usually involve quite a bit of cost - a sweep of the chimney and any repairs to the flue are just the first, and then it's not just the cost of an inset but also a proper hearth to meet regulations. So in your position I would dress it up for now and then when savings permit, get a specialist who can advise about safety and regulations. So to make it look prettier - I reckon you've got a stunning surround under that white paint. If you're happy with it being black, then strip the paint off (with one of the gels) and then polish it up with some "black grate polish". All the detailing on the surround will look stunning. I'll send a photo of one from my last house. With all that detail, I'd then just cover the bare bricks with some ply and paint it black. You could do a fake hearth with some wood painted black if you really want a hearth. I'd then get some nice big candles to go in the recess and forget about it. If you start getting a lot of dirt coming down, you will probably need to get the chimney swept.