Oh, and do you have a color scheme in mind for the chair and rug?

I'm trying to stay away from blues and greys in this room. Yellows, corals, oranges.... ? Arg.

IMO a rug should not cover the entire floor and I like to have 3’ around all the sides of the table so the rug size you are thinking is too much coverage for the floor and too short for the ends of the table . Maybe try no rug it might help with the more casual look you are wanting. I sure hope you are not doing benches for seating .

No rug - you don't have room for a properly sized one. They need to be 36-42" larger than the table top on all sides yet not run into your baseboards or any furniture placed against the walls. Fabric at the windows and on the chairs will have to be the soft touch here.

Is it weird to have no rug? Yes I was worried that the right sized rug for the table would be too big for the room. Should I have gotten a smaller table? I think I am entitled to swap it out for the next size smaller if I want. The trade off is that I liked that this table could seat 8 without leaves.

I think this West Elm chair is cool and could work but I’d prefer a different fabric. Thoughts?

You can have a piece of carpet bound, and that way it can be just the right size for the space. Seagrass would be nice. I believe you can get custom-sized Fibreworks seagrass rugs from Pottery Barn in the US (I'm in Canada).

The table is 84”x44”. I’m a dummy! So I need 9x6 rug. I was off my rocker before?!

Ugh I mean 11x8.

84 +72 and 44 +72 =

13 ft x 9.5 - 10ft for the size of the rug, however that visually seems too large for a 14 x 14 room, so I would settle for a 9x12 rug.

I'd select a rug with NO border.

A continuous field will make the room stay large in appearance.