Claire, nope they are all level. But maybe you’re seeing the gaps in between the planks that are typical for old floors. We choose to not fill them in. They still have to finish the toe trim.

An inspection is required to determine what would need to be done. For example, I've lived in a number of older dwellings whose plumbing and electrical were original and it did not mean I had to replace it because It was unsafe or old. In some cases I chose to update...but did it over many years as I had time, or in conjunction with remodeling parts of that house. I'm not saying the OP shouldn't look at updating; however, I am making clear that this is not something that necessarily needs doing immediately.

Another thought to "updating" is considering a different layout for your furniture. Hard to tell from your pics if this is possible but sometimes moving pieces around gives a "fresh" feel to the space. For example, the tall piece angled in the corner could be set straight on the wall leaving space on the window wall for a large piece of art. As others mentioned, I'd think of lightening the walls and adding contemporary decor rather than worry about styles not "matching". My first thought was replacing the bedside lamps with a more streamlined yet classic type like simple gourd lamps. Your furniture is beautiful and a lovely warm wood tone on my monitor.

To me, it looks like they used self-sticking drywall tape (the stuff where you see the dots) and then coated the walls with a thin layer of textured quickrete. Is the piece that’s broken away very hard if you try to break it?