"can 11.5 x 16 work for dining?" That's going to be hard for anyone else to answer without seeing your floor plan, because you may need to account for walkways, door swings, etc. (Also we don't know the size and shape of the table you are trying to fit, how many people you want to seat, or if there will be other furniture in the room.) In general, I've seen guidelines of 30" to 48" from table edge to wall, with 30" being the minimum and more being better. Horizontally at least 24" per person with more at the ends (for leg room), and possibly more depending on the size of your chairs and your guests. Create a layout drawn to scale, with your table drawn to scale in it.

Is this for your everyday table needs? Or if it is for entertaining guests, how many do you want to seat at one time? How many people do you want to seat in front of the TV? That's a small table 42" x 30". If you imagine using a 24" width X 12" depth place mat for each person, you see that your table fits 4 people (one on each side) with a 6 inch space down the middle for serving dishes. There's no point in having all that bench seating if the table only fits 4. Consider getting 4 chairs - much more comfortable than bench seats. Be aware that living room side chairs sometimes have the wrong seat height to use as a dining chair. And if your table has a box apron all around, the arms may not fit under the table.

Looks like you have room for it. Maybe add an end table with lamp in the corner between the sofa and the chair? I can’t tell if the bookcases interfere with the doorways…might need to ditch them and go for big art on the walls. I can’t tell. What you could do is wait on the bookcases. Kludge some cardboard together to mock up the bookcases and live with that a bit before buying/building them.

You want at least the front feet of your couch on the rug. Look carefully at Beverly’s post. You don’t need the entire couch on the rug, or you can have everything on the rug. She’s also showing you different rug sizes that work with different pieces of furniture. Use painter’s tape to plot out a size you think you want before buying anything.