I don't know about No. 1. I caught Tenny laying in the box...which is right next to my lovely comfy bed..so, go figure?

As to No.2...I think it is a way of marking. With the added info about not covering her poops, I really think it is so. Cats have scent markers in their paws...in fact this is SOME of the reasons cats sharpen thier claws on things, to release the scent on the item they are scratching. This is why even declawed cats do it too/still. So, when kitty poops, she then marks the area around it as if to say, "this is my poop, and I don't have to worry about it". This would differentiate her poop, or her food, or her special something from other's cats...who would then mark their territory with their scent. I would guess if she is doing it infrequently it might be that something stressful has happened, or she is feeling insecure about something, and feels the need to revert back to her wilder days- even if she never knew wild days.

My cats sometimes do this, even to the side of the box, walls, etc. I have had some of my kitties from birth..so, I know it isn't anything traumatic related with them...and it most certainly is NOT a physical problem for them...like injury, change in litter, etc.