You should have minimum 5 ft but 6 ft is ideal. I've played pool where tables are 4 ft from the wall and it is too close. The standard pool cue length is 57" and the draw length is about 6" so 5 to 6 ft would be ideal.

A quick fix for the dining room would be to center your dining room table in the dining room area. You can define this room a bit more clearly by adding a chandelier centered above the table. For the living room, the loveseat can remain on where it is, but pull it away from the wall. Move the loveseat so it more to the right, it does not need to be centered under the window. Place the larger 3 seater couch along the wall where the coffee table currently stands. It should rest under the window about a foot away from the wall. Place the side table at the corner between the now perpendicular sofas and center the coffee table in the room. This will give you space for a nice entertainment unit where the large sofa previously stood. Alternatively you could place a credenza here to store your dining room dishes or additional storage. Lower the painting on the wall to eye level so the center of the painting is at 54" above the finished floor. Purchasing new window treatments or drapery panels that coordinate with a new throw and cushions for the sofas will tie the elements of the space together and make it more cohesive.

I would for sure spend the money to remove the wall and I think the idea of a large island with stools is great if you have the space it is hard to tell from the pics a floor plan woulf be very helpful and maybe some more pics from different perspectives also.

squeakerd - it is really hard to get a perspective on the whole area but if this is part of a much larger area then I feel you need to first decide just what you want as the end result. Do you just want your entire area to be one open plan or do you want to break it down into visually defined areas within the open plan. As you have the area now, I don't feel any cohesiveness between your table and the sideboard, I think I would move the sideboard to the end wall, it looks more like it would belong there, even just by the shape of the room. Definitely a larger rug will define the space better - just be careful of any trip hazard with the door nearby - but before you decide on the rug, consider window dressings and whether you want things plain or introduce some bold patterns and what colours look best in the area. Artwork can go where your sideboard is now, but again think colours and impact of design on the whole area. It is all very well to build a room around one piece, but you need to look at the impact that piece will have on other items and what limitations it could cause. I would suggest you set aside some serious time to look through photos on Houzz, especially if you can find areas similar to yours, till you find what appeals to you, put the photos into your ideas book and use that to build your room. I have found this invaluable in the past and it has saved me many an expensive mistake.