Please post a scaled floorpan at least of the kitchen and dining room, ideally of the whole house. You'll get better replies with more information.

Looks like a nice little compact kitchen. If you are moving appliances and plumbing in the future, I’d suggest locating the stove somewhere not under a window and adding a vent.

Cleaning grease spatter from a window is not ideal. Agree with nixing the corner sink. As stated above, a diagram of the entire space you have to work with would be helpful.

Unfortunately, this is the best I can do with regard to a floorplan.

Yes, the fridge is enormous and we will definitely replace it with a smaller one, likely counter-depth. I think we could move the door to the dining room.

cawaps suggestion to eliminate the kitchen door is a good one.

I played with the plan a bit to show you what might be possible if you changed door and window locations on the back wall, reusing the existing windows and door.

I eliminated the window on the side wall, moving it to the kitchen door's opening. I moved the door just to the right of the kitchen and shifted the DR window to the right.

I created a banquette in the dining room, similar to these banquettes:

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A banquette makes the best use of space in your small dining room and provides additional storage. It allows a decent aisle between table and stairway wall.

I added stud space pantry storage on the stairway wall, similar to this:

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You might also be able to go with deeper pantry cabs like this here but without more measurements, I can't determine that.

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I swapped out that huge fridge for a 33" CD (counter depth) fridge. I placed a small countertop MW above the counter like this:

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The GE Spacemaker II MW is designed to fit in an upper cabinet.

I added a 36" Super Susan for pots and pans storage with a pull-out for oils and vinegars next to the range. Here's mine:

I voided the corner storage in the upper left corner to make room for a drawer base next to the range to give you storage for pot holders, cooking utensils, etc.

I placed the sink under the far right window with the DW to its right, giving you a generous stretch of counter between sink and corner for prep.

I did not add a peninsula to the above plan. There isn't enough room to add a peninsula longer than about 51" without impacting the kitchen entry, creating a potential bottleneck when the fridge door is open. I also didn't think a peninsula added enough counter space, storage and function to make the trade-off worth it, especially since it would require moving the sink to the left, shrinking the prep area between sink and range. Adding a peninsula would also impact the aisle between it and the table when the table is extended for company (blue line approximates an extended table).

The above is just to give you an idea what would be possible with a few structural changes to door and window placement. Once you're in the home and closer to tackling a remodel, come on back with a measured drawing and we'll help you come up with preliminary plans.

Meant to include this image too.

This suggestion removes the pony wall, eliminates your back window to create a wall for the fridge, keeps the back door, puts the sink under the window and moves the range on the bathroom wall. If you're not devoted to gas cooking, you might consider switching to a ceramic top electric. In a small kitchen, a ceramic top was very useful to me as additional work space.

Your dining space is a nice size, I'd protect it and not extend the kitchen into it in any way.

These drawings are using the Ikea planner. there's an 18" pull out cabinet to the left of the sink that represents your dishwasher. Standard Ikea sizes look like they fit nicely into this space.