How old is your GCC? I think that most people get their birds at such a young age that it would be best to fix any issue with the way that they have been clipped as soon as possible, but if your bird is older than the usual bird it is possible that he is about to molt so I would not mess with any of the feathers on the side that was clipped, but I think that I would still even then on the other wing so that he can regain some control over his flight.
The behavior that you describe may be incomplete or not as it does not include the position of his bodily contour feathers nor what he is doing with his beak. Again his age could make a difference as well. This could be that he is claiming whatever he is on as his or it could be asking for food or attention. A video would be helpful to see what he is doing.
I keep a roll of toilet paper on hand and some rolled up in a pocket for emergencies. I don't use paper towels as the toilet paper is much smaller and cheaper. Paper towels are too large and thick, they are like overkill for a little poop. Now since you bring it up I do not recommend potty training a bird for any reason. Please read this as well as the link contained in it,
viewtopic.php?f=8&t=13918 In regards to your birds behavior with your mom, It appears that he may have chosen her as his favorite human and this also suggests to me that he is older than the baby bird that most people usually get. If you find that who he is most bonded with to be a problem then you would have to keep him and your mom away from each other, watch while he goes into depression while you do all that you can to encourage him to rebond with you and maybe he will rebond with you after he has finished grieving the loss of your mom, but then as soon as he sees her again he is very likely to choose her once again. Still working on building his trust in you and your relationship with you as being his second favorite person is a good thing to do and may very well eliminate his poor behavior towards you over time.
There are several reasons that I am perhaps not the best person to reply on this issue of pellets as I do not like them and do not feed them to any of my birds. Instead I feed fresh raw fruits and vegetables and gloop for their breakfast as well as for all day long and a quality seed mix for their dinner.
Toys are a rather humorous issue in many regards and I do supply my birds with things to use and destroy as toys. Birds in their natural setting do not have toys but they do practice on their foraging techniques and they do practice their self defence, well some of them do, but no toys. I supply my birds with a variety of toys for foraging and some just for them to destroy, but the thing with toys is that they tend to be afraid of them at first and then you must teach them what they are as well as how to use them. This is accomplished by playing with these toys yourself. If the toy can be taken apart, then sit in front of him and take it apart and put it back together over and over until he demands to play with it himself. This holds true regardless of the toy type that you choose for them, play with it with them watching until they want it enough to try to take it from you.