Regarding your chicken - sauces with sugar will caramelize and most likely burn onto your pan if left long enough to cook foods.
Because of this I save my sauces for after the meat/food is cooked and out of the pan. You'll find the same 'issue' when BBQing, etc. If you don't want the mess and char save the sauce, marinate in vinegars, wine or other acidic mediums. Then glaze with your sweetened sauce and pop into a hot
oven to reduce the sauce to a nice sticky coating.
For cleaning your current burnt on mess, heat your pan on the stove, add some fat and when it is melted use a metal kitchen pad (without any cleaner) I use those cheap copper pads. Now rub off all that burnt on gunk, your fat will turn to a thick black oil. Use a paper towel to wipe it all out and then add some new fat back in and allow it to heat up. When your satisfied with the condition of your pan turn off the heat, and your good to go.
As for potatoes, they can be messy. Yours are over cooking, I would suggests cutting them into small cubes (half of a domino in size), add a lid to steam and when they start to slightly brown remove them from the pan. Cook them al dente like you would spaghetti, so you can pierce them, not mushy but not hard either.
Try slicing rings of onion to place in the bottom of your pan (with your fat) and start your potatoes on top of them (with lid), steam until the potatoes are partially done, then flip and stir them to brown, and remove. Food continues to cook a few minutes after removing from the heat. So remove your potatoes to a warm container with a lid and let sit for 5 minutes before eating if you like them mushier.
I hope this helps ~