I would put hardwood floors throughout the area but I am partial to hardwood and know it’s not budget friendly. You could use rugs to create distinct areas — one for dining and then one with the couch you float. Then choose a curtain to coordinate with rugs. Then pull a couch color from the rug (I believe in choosing your favorite color for a couch unless doing a white slipcover which actually has been my best couch with kids because BLEACH haha. Most couches today just don’t last forever anyways — get something you will love). Then choose an accent colors for toss pillows, get an end table and some lamps, and a chair in your accent color. Art. Then paint. And maybe think about painting the brick and wait until the other elements come together to see how you feel about it. I think you would feel a lot better about the space if it looks more put together. Then for your storage, you could get ikea sektion cabinets or something like that and even paint them to have more attractive storage and there are even hacks to make them look more built in. I’ve hacked several ikea things in my house (closets, playroom storage, a bookcase.. and I am not a DIY person at all LOL but custom storage is so expensive and if it’s not in areas where I entertain or my kids are just going to beat it up, no way am I doing anything custom) you could maybe even add “mudroom cabinets” because your garage door leads into the dining room correct? You could totally hack ikea pax into mudroom cabinets if on a tight budget/. You could maybe also add a pantry cabinet if you need extra storage (I don’t think I saw a pantry in your drawing and this is where getting the full floor detail is really helpful!!) if you can better think about what you need, you can probably get more advice about what to do with that area.

As several have observed, it likely to be a stiffener for the wall, although it is overkill for that purpose. However, there is the possibility that it was installed to stiffen the floor. Not possible to tell unless the subfloor is removed and floor framing examined. If the rim joist is doubled or tripled, then it has no structural purpose. If not, consider adding a rim joist once the wall is removed. If you do install a cable railing, make sure at least one center post runs floor to ceiling - two would be better - otherwise anyone leaning on the railing might be in for nasty surprise. I hope you pulled a permit for this.

You didn't give the one photo that we would need to see in order to make a guess. I can't tell if your gable end truss at the middle section with the taller plate line is the wall you want to remove. Either need more pix or put the windows on your floor plan with their size callouts

Yes, those studs are load bearing in that they support the weight of whoever is on the landing and stairs. But, you can still do what you want, just frame the opening like a door or window would be framed to support the load above them. You should be able to take out the two middle free-standing studs, install a double 2x6 header across the top and support each end of the header with a 2x stud. Then fill in your doggy door as you desire.