So I would absolutely keep the rug. I would do a cooler color on the wall like a gray green or gray blue. Get a runner to go between the doors that coordinates with your existing rug. I would add real baseboards but if you can’t just paint a 4” wide white band above what you have to fake it. Add a narrow console table with an open decorative front to hide the air conditioner. Paint the door to the house charcoal gray. I found these curtain panels that to me could mimic artwork to hide the vertical blinds. Then add a seating are there. Keep the bench and mirror as is. I don’t have photoshop so excuse my poor mockups lol.

As for the gap to the right of the steps, I see two possible solutions. One is to make a narrow brick raised bed in which you could plant something. The second is to put a trellis on the wall and grow something skinny, such as one of the clematis cultivars that will grow in shade. This would involve some research, but 'Betty Corning' might be one of them. Now, as for the downspout, I see the solution as going underground under your sidewalk and out to the lawn. I have two of these, but mine don't go under any concrete. It won't require anything underground in the way of a drywell or something, it just needs to have a pipe that goes up to the lawn with a little drain cover that you can take off to remove any debris like seeds or leaves that get in there. If you go this route, you will have to periodically inspect your gutter to make sure that nothing is accumulating up there that might clog your underground drain. As long as you do that, the system will work quite well. I agree with the other posters that you need some professional help with this.

Hello, fellow Texan! I understand your dilemma — our front door area gets afternoon/evening sun, too. These triple digits and searing, scorching sun are brutal. I burned my hand on our door handle recently. It’s hard to say about trim color without seeing the entire house. I’d love to change our front door and trim color to something darker, but it would quickly fade. I can’t see your yard but am wondering if some landscape changes might provide a more welcoming feel coming up to your entry? You could also have some colorful pots out (Talavera, glazed pots, etc) with hardy plants like lantana and portulaca. I usually have mandevilla in pots out front — they got burned up this summer. What style(s) of decorating do you like? Have you saved any inspiration photos?

" is there a way to tie the window and doors together without having to cut concrete? " No. I do not think that is concrete but there is definitely a header between the door and the round top unit. You "could" reframe the entire wall, redo the interior and exterior finishes but then you would be stuck with the fact that the round top is narrower than the door unit and will look awful set on top. Leave well enough alone until you save enough to get rid of the round top and the double door.