well officially 3 weeks taking care this kitten. As i am new to cat, do a lot of studies and also checked this topic occasionally.
bought:
1) litter box x 2 with clumping clay type, scoop and etc relevant to litter
2) single level cage but not too small size (put 1 litter box, food&water tray, 1 container as his bed)
3) food, Blackwood kitten
4) small toy and cushions for him at this favourite spots
we thought he was not familiar with litter box for peepoo and even tried to stimulate his anus
that's why so happy to see him pee and poo in the litter box after we prepared for him. However was once poo on the floor maybe because of diarrhea. Sometimes poo near to the edge of litter box as well. But we are fine because no pee poo other than litter boxes.
Bought BW kitten to him after finished the RC 'Recovery' and he likes it very much. No wet food since then and texture of poo is ok and good flow. He did poo frequently (more than 6 times a day) during full wet food and therefore vet suggested to feed him only dry food during the 2nd vet visit.
For the first few days, we let him roam around if we at home and caged him during our outing. We monitored over a weekend to check his behavior and found out he was not happy with cage. He bite the cage, climbed up and down inside. However he did good outside the cage and thus we decided to let him free even no people at home. Cage is just for night sleeping time. For the past 2 weeks, he is totally OK! No mess and damage to the home.
Anyway, he is super active and playful. Likes to bite our foot and hands. i guest he is just too small to stay calm and chill. Brought a lot of laughter to us and we are happy with his presence
Future plan, feed him well then get him vaccinated and will arrange neutering whenever the time is right.

Day 1
Wah very detailed write up. The biting is normally because the kitten wasn't weaned off properly by the mother. My cat around 4 months now still like that. Dunno if it will ever stop... But controlled bite at least. Its always stressful to get a new kitten. But congrats and seems you both are having a lot of fun 😁