That is a whole lot of question, there, and difficult to comment on the unseen furn. pieces, but a couple thoughts to start the ball rolling: Yes, you can combine patterns.Take your major colors (navy, white , red/orange) and look for patterns of different sizes and percentages:70% navy in a toile,20%navy in a stripe, etc. Gather your softgood selections together before selecting paint shades,for better accuracy in wall color. Carry colors into the kitchen by painting your chairs, and through softgood display ( tablecloth, towels, apron) as well as everyday work items routinely left out. Keep trim colour the same thoughout the space. You might slipcover the chairs at the ends of the table in a different fabric, but rather than a pattern, consider a plain fabric w accents like a monogram or stamped design to transition from the remaining patterned chairs to the couch slipcover. In general, I'd shy from painting large pieces black in a small space, but without knowing your other selections, can not make specific suggestions.( I wonder if navy might look well, when all is put together? Perhaps your fabric choices will be so sharp that a neutral off-white is begged for...) Continue to post as you make decisions, and more folks will join in. Looking forwad to seeing what you decide!

I think you could get the telly put over the fireplace. Might need a mantle to deflect radiant heat, not sure. But on the cables and power, I imagine they can get that sorted. Im guessing there is a wall behind you when you took the photos. I agree that a low corner modular sofa would look great. Just don't get it so long that it is up against the fireplace wall. Placed into that corner of end and piano walls . Then pop your cute chair where the sofa is now. Large ( big enough for the sofa front legs sit on it, I'm guessing 2x3m or even 3x4m) patterned rug to define the area. Can you move the piano to another room or against the computer area wall? Can you make the small windowed room the homework hub? Imagine a long bench against the window ( Ikea do a good cheap range that you make to fit your space). Ensuring the computers are in line of sight from the kitchen(?). Pull out the table to give it more space around it. Or flip it to run the other direction. Hard to tell from the pics the dimensions. Paint a lighter shade as mentioned before. A sketch of your floorplan would be really helpful :)

I would suggest you do not make the area open plan. You should make the dining room a dedicated home office/study area. You could install desks and plenty of bookshelves for storage. Sort through all your stuff and try to make the family room and dining table for eating, not stationery. You could definitely make the corner where the bookcase is, into a study area as well.

I think one of your key considerations will be what to do with the flue / chimney. My personal thought is that you should look to punch it through the wall and keep clean lines inside, but not sure if that is feasible for you. Otherwise you might want to make a feature out of the chimney enclosure - use it to break up the length of the room. The path you choose here will inform the remaining design decisions. You have to keep in mind that an off-the-shelf fireplace unit is not going to have heaps of flexibility in terms of altering its design to suit your space. If the unit you are looking at is designed with a vertical flue and you want to punch through the wall instead, you are going to need specialist advice to make sure that the gas certification for the fireplace unit is not compromised by your alterations - or chose a different unit that suits your needs.