Hi. I think it would help to see the rest of the room and the layout ie i.e. Can the tv go elsewhere? I think your eyes are drawn to the window so you may find a blind will help. Ignore the bits I've added but I think a tall piece of art will help draw your eye to the fire so it becomes the focal point and I think a chair will help. I'm not sure if this is what you meant by balance the wall though or whether it would work in your room

You could have a tall narrow mirror (rectangular or oval) centred on the tap, and therefore narrower than the sink. Or, you could cover the whole wall to the edge of the window cill in mirror. Perhaps built out on a slight frame to cover the boxed pipework too. This could be made to measure or you coujd do it on a budget with mirror tiles. Either way you could divide it with a shelf or two. Another option would be to create a mirror wall incorporating an integral cabinet, using the space you'd get building the wall out to frame the boxed pipework.

No. You can have panelling that goes two thirds the way up the wall topped with a shelf (like an upside down skirting board if that makes any sense). You can also have it over the panelling in line with a horizontal board. There are lots of different versions.

I agree you don’t have to be symmetrical. I did a sitting room for a client recently and had to work around an off centre window and a panel heater. By the time the room was painted and furnished the asymmetrical design wasn’t obvious. What I would say about your drawing tho is that the panel round the mirror is very tight. That maybe dictated by the width of the tv on the right but if you had room to widen it, it would look better. Are you set on having the tv in the wall? Or could it be on a floorstanding unit/table/other (something sympathetic to the style of the room)?