Here’s some copyable examples of lists using images or emojis for your checked and unchecked status. It’s not exactly what you are looking for, but might help you get some ideas.
A checklist style layout is probably not the best if you want them to reoccur.
I also don’t quite understand why you aren’t getting the checkbox to show as checked or not. You should be able to tap directly on the checkbox to check it and it will fill the column you have set for your checked value as true or false. If you are going into the details of the list item and clicking a button, then it should be writing true or false to that same column. I don’t know if you are maybe setting some other value other than true or false.
Instead, to get the reoccurring part to work, I would use a regular inline list with an image or emoji and have it set up so either tapping on the list item, or going into the details and clicking a button will write a timestamp of the current date/time to one of the columns. Then create an IF column that will check if that timestamp is WITHIN TODAY. If it is, then return the image url or emoji for a checked status. Else return an image url or emoji for an unchecked status. That way after midnight, the image will change and reset to unchecked and once you reset the timestamp, it will show as checked until the next day.
My example above uses Unique ID’s instead of timestamps, but the general idea is the same. You can simplify what I did quite a bit and ignore the whole Reset Multiple part.