I would be inclined to go with an unobtrusive light since it's the living room and anything too dramatic or a hanging pendant may interfere with your peripheral vision (or otherwise be an annoyance) when you're watching TV, etc. Also, being so near the sliding door, the wind may cause a hanging pendant to swing quite a bit which will cause the lighting to be constantly shifting and changing which I would personally find annoying. I'd go with something simple and subtle, but look at getting a tall standing lamp for the corner near the sofa (or possibly at the other end of the floating TV cabinet). In terms of warming up the apartment, I think you need something on the bare walls. A smaller picture above the floating TV cabinet will help to take the focus off your TV. A larger art work behind the sofa will also help to add some colour and personality, especially if it picks up some hues from your sofa. If you don't like the little Buddha statue, I would look at adding one or two other items that you do like (perhaps picking up colours from the wall art) and making a little vignette. A couple of colourful cushions and a storage solution for the wires, games console, etc on the floor would also help to bring everything together. Something as simple as a woven basket under the floating TV cabinet might help to keep the games console, etc in place unless it is in use.

practicallity wise with young kids shaggy is going to be a nightmare ..wool is good as warm in Winter..and hypoallergenic.. Harvey Norman have great rug sales sometimes 40% off just keep an eye out for them.. I don't buy wool I just buy what looks nice and is practical.. 2 of my kids have eczema and they find wool rugs rough and itchy..we used to have a wool rug at our old place..so I only buy synthetic now..

I agree about the idea of putting roller blinds on your door , matching the colours of the others must mention about Annie Sloan paint : it is a chalk paint and you can apply it on any wood surface with at having to use primer, what " seals" the pain is the Annie Sloan wax you apply afterwards. You can Buy Annie Sloan on line , i use Annie Sloan a lot.it is expensive if you want the legs painted black to be smooth, just paint and wax , but one coat of Annie Sloan does not give a good coverage. It you want it " distressed" slightly, then just sand a few it on the edges afterwards, before the waxing With a slight " distressed" leg look, but you would need to give the top of the table a light sanding to " rough it up" on the edges if you want a good solid, coverage, Annie Sloan is not the right choice have a look on eBay, I have just bought some cages light to fit near my table outside ( I was just playing around with them yesterday before the electrician comes toda), they were only like $46 each

Though I don't know for certain, I think the cotton/linen shades are removable. I wasn't able to determine this by my searches. This could easily be confirmed by making an enquiry to supplier before purchase. Alternatively, a handmade one could be made removable by making shade slightly larger than frame and making ties.