Misc. questions:

1. farmhouse table- stain darker and paint base (either white or black)

2.  flooring- I would not do a wood tile against the hardwood, I'd try something that will contrast a little more like a slate looking tile possibly.  

3. rug- I would consider getting a matching long, runner version of whatever rug you go with for living room and use it in the kitchen in front of the cabinets on the window side.

 

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Open shelving might be nice to add on right wall where coffee bar area is.

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Love this inspo for your coffee bar area- adding stools for extra seating

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Farmhouse table- white base/dark stain on top with black chairs

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Also love this little shelf above kitchen window and the jute rug for kitchen.

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Use the same window treatments on the door in here as you are getting for the doors in the living room and you can also use the same curtain rod for those and the valance over the windows.  I would probably leave the other two small windows empty (on each side of the door) or do the exact same valance on those as in the kitchen window.  One more option would be to do just a simple woven shade (like this) on those windows too and no curtain or valance. Definitely yes to a "farmhouse" or similar style sign for above the door or window. 

Kichler Merlot light over dining table and a coordinating flush mount to replace ceiling fan in kitchen area.

Simple runner on table with tray at the center and a large vase/jar on top with some florals.  Optional: set the table with white dishes and stack other dishes/chargers underneath if you want. Choose some simple solid napkins to match with the runner for placesettings too. Definitely yes to a "farmhouse" or similar style sign for above the door or window. 

These curtains are definitely my top choice.  They are only available in a longer length than you would need right now but we could easily hem them.  I prefer the tab top curtains over the grommet top because I just think it hangs better and looks more expensive.  I've linked a few other curtain options that I also like below.  Also I've linked a few curtain rod options below, the first being my favorite.  I also like to use the curtain ring/clips when I can because they help the curtains drape so much better.

I am leaning toward a rug with more texture and a simple pattern (a shag or jute/woven possibly) since we have curtains in here that have a very busy pattern.  I've linked lots of options below that I think would work and I'd probably lean toward an 8 x 10 size or something around there.  I've also linked some printed options below that I think would coordinate with the curtains if you would rather have that.  I think since the curtains and rug aren't right beside each other it would be fine to have coordinating patterns, but a more simple rug would allow us to do more with accessories and pillows.  

I think we can probably work with most of your existing pillows but I would overall use a mix of grays, creams/whites, and navy pillows with lots of different textures for both the seating area and the window seat.  Pillows are something I often get a Homegoods but I've also linked some Target options below:

   We can find a few things to go on each side of the television to balance out the space- I usually prefer two matching objects (vases, candlesticks, or lanterns).  I've listed a few inspiration photos below.  Also this is totally optional, but I do think it would make a huge difference to resurface or paint over the stone panels/inserts in the fireplace so it's a little more updated/farmhouse style.  Those seem very fancy/kind of 90s style to me and since it's the centerpiece of the room I thought it would be something to consider.  I didn't get to look at what material they were but here are some possible options:

1. painting over the stone insets so everything is white/one color

2. covering it with wood/shiplap and painting everything white/one color

3. tearing it out and reworking the paneling/finish

Some examples of the look I was picturing below:

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I would stick to a very neutral cushion in a linen-like or woven fabric with a little texture- like pictured below and then we can add some cute pillows in creams/whites, tans/grays, and navy.

Gallery wall over couch in living room (I can use what you have first and fill in/purchase new pieces where needed)

Mirror/larger piece in entryway

Window with wreath over console table in living room