Well I expect my teenager to cook simple meals, do some laundry and keep his room clean. But given he’s currently still a baby I expect him to work hard at drinking milk, giving the best cuddles and smiling lots. I’d like to add sleeping to the list but I’m not winning that battle. Expectations grow with our children. Right now your STBXW is sending him to school appropriately dressed.
As for your other points (as you asked):
Does tidying the "toy" room improve anything
Yes. It is hard to clean a room properly if it is so untidy you can’t get to the floor to vacuum. Personally I clean daily because we have pets but if you don’t I’d probably consider a weekly tidy and clean to be sufficient. You might have other considerations of course. Cleaning is important for hygiene reasons, and general checking/maintenance on the fabric of the building and the furnishings. So yes, tidying the toy room is important. I’d expect a six year old to help me tidy but not necessarily to be able to manage such a task alone (it depends on the size of the room and type of toys I guess).
does me asking him to make his bed improve anything,
Not really. Again I’d want bedding cleaned regularly and checked for wear. Personally I like beds made for the joy of getting into them at night and folded back to air during breakfast. If a child’s bed stays airing all day that’s fine.
does me asking him to hang up his towel improve anything,
Yes. Wet towels that aren’t hung to dry will soon start to smell. A six year old can hang a towel but I’d probably check it’s hung straight enough to dry completely.
does him taking his plate from the table to the kitchen improve anything?
Yes. Again hygiene.
Absolutely not, does him saying please, or thank you improve anything?
Yes. Basic manners are important for social reasons.
You seem very hung up on trying to micromanage how your ex wife parents your child. Perhaps reflecting on this controlling nature will help improve your next relationship.