The lower price makes it likely to be polypropylene. Was it the only one like it in the store? Seems odd to not have a label on the back. Could you go back to the store, see if there is a similar one and check to see if it has a label? Is there a manufacturer's label on it, or NO label at all? If there is a manufacturer's label, put any info on it in this post, and that may allow us to determine what it's made of, especially if there is a name of the maker or the rug. http://www.doityourself.com/stry/how-to-clean-polypropylene-rugs

A 6x9 rug is pretty large and pretty heavy. There really is no need for a rug pad underneath (at least not from the perspective of 'holding it place'. One of my favourite places to shop reasonably priced rugs: Ikea. They have HUNDREDS and they will have the backing listed as well as the fibre content. If you have an Ikea near you, you are welcome to visit (assuming they are open...most are with mask requirements of course). You can look at the back of the rug to see what it is made of.

Sounds like a fireplace re-do might be a longer-term fix. In the meantime, I'd paint the mantle a dark brown, a similar colour to your end tables. It's not trim and shouldn't be white. It pops out too much in the white colour. Another idea that doesn't involve any ripping-out is to go right over the existing mantle using a mantle slipcover in wood. Here's one of many how-to's on the internet. If you stained your brick as well, you could have a whole new look. https://www.fwmadebycarli.com/2011/01/making-of-slip-covered-mantel.html

when I first saw the pictures I thought you need to bring the sectional closer to the fireplace and TV.... then saw it was a step down from the dining area. kind of dangerous to do that. maybe you could find a taller bookcase or 2 to place on the lower level and serve as a sofa table, bar and buffet when needed blocking off the step down and getting more storage and flat surface. I think in this case you do need a rug to get some color in the room. make sure it is large enough so that when you pull the chairs away from it that they are still on the rug. pull your favorite colors from the painting to bring somehow into each area (kitchen, dining and living room). looks like you already have some red in the kitchen picture. it should be repeated throughout the whole area that is visible in an open concept area. the pictures are just to give you an idea how just small things in each room repeating a color help make it interesting, unified and keeps your eyes moving in the room. you have so many choices to pick from. what is your favorite? I think changing the rug in the living room would also help. 2 rugs don't need to be the same but should complement eachother.