Have an electrician take down the old light and take a look at the connection. You might need a stronger box, or not. That is a simple fix. Our small LR fan came with the DW but we did have a larger fan/lights installed last year. I think he may have replaced the box. As an aside, Don't put a fan anywhere near the kitchen stove if it is gas. Could blow the flame out, even on low fan setting. I couldn't use my fan in our last house when I needed it most - hot humid days :-(.

First, the green wire on the switch is for grounding, and must be connected to a green or bare copper wire from the wall. If you don't have one of those, you'll either need to rewire, or purchase a switch that doesn't require a ground. White wires (neutrals) should be left alone. There is not enough information provided to tell you about how the other wires should be connected. In a typical set up, one of the black wires in one cable is your supply. The other black and the red will be in a second cable and will go to the fan/light combination. The instructions in the switch package will tell you which wire should be connected to which. There's no guarantee that the new and old switch will follow the same wire color scheme. Make sure that all of your connections are tightly made using approved wire nuts.

Have you looked in to universal remotes for ceiling fan and light? Ask at your local lighting shop. https://www.amazon.com/Universal-Ceiling-Fan-Remote-Control/dp/B00A2WU4CK

I read there were other lights, that's why I referenced this: If you don't like fans, abandon the ceiling box. Most likely, the fan light is over foot space or non-main circulation space. A recessed light will compete and detract from the accent wall eyeball light(s) and perimeter lights that creates a mood behind/around the seating area, where a central light will just blast light down and hit your foot space or the corner of the coffee table. All assumptions without good pics and more information, but those assumptions are standard fare for living rooms (see I assumed there were 4 "corner" lights and was right). A hanging fixture, however, will diffuse light better and fit the inner seating area better for the mood if you choose to have some central light there. I don't participate in decor advice, but other commenters may visit and have great ideas to offer on what fixture.