Hi, welcome to the forum! Glad you joined!
Recently I have purchased a chicken coop for 20 chickens that looks like the image above.
How big, in feet, is that coop? Just because it was advertised for 20 chickens does not mean it is big enough for 20 unless your run is totally predator proof and you never lock the chickens in it. Then it might do as long as your weather doesn't lock them in the coop for too long.
1. Cannot get in the coop to clean under the roost that is at the other end (opening over there is in the middle and currently has auto door). The system came with two 1 x 3 roosting bars that were closer than 6 inches apart so i exchanged that for one long 2x4 and that is working successfully. I have under that area barn lime and clean out daily except for that darn back corner.
If it can work, a garden hoe is a good idea. Not sure what your coop floor looks like. I'd be tempted to cut a door or access panel down on that end so it is accessible.
2. My windows do not open, just plexiglass. I know I can replace with windows that work but I do not want to spend 100$ on windows
What is your concern? Ventilation? What kind of ventilation do you have now? Openings under the overhang and covered with hardware cloth to keep predators out can really help. Gable vents or roof vents can help. A vent fairly low on the end away from the roosts could help.
If your concern is not ventilation, what is it?
3. The chickens do not like the top opening of the hen boxes and have decided to lay eggs elsewhere (mine are 100% free range). I was wondering if y'all have had similar issues and what your fixes would be.
If you can, lock them in the coop only for a week or more to teach them to lay there. Maybe that will be in the nests.
When I catch a hen laying an egg where I do not want her to I lock her in one of my nests until she lays that egg. I usually only have to do that once to each hen for her to learn where to lay.