My guys would dig hole after hole after hole for days, and not use them. Trying to dig holes is a good sign. Eventually one day the light bulb will go off and he'll "get" it. Every so often, if you see hm in the litter digging a hole, go over and use your finger to fill it up like he eventually will. He'll figure it out.
I don't know if that paint box thing will be big enough to carry an inch or two of litter, and he may get it all over the place. If there isn't enough litter to cover, especially with the clay, it will smell. You also don't want him peeing off the side, and getting used to doing that.
If you go to the dollar store (if you have them near you) you might find a tupperware box or some of those aluminum cake pans that will serve you better until you can get a bigger litter box. He's small, so you don't need a big one yet. You might even find a small one at the dollar store. Or, look for one of those dish pans you would put in the sink.
Tell your boyfriend the reason for not using clumping litter with kittens is because when they are that little, they play in the litter a lot (as you have seen) and because of that, they end up getting it on them, licking it off, sometimes even eating it.
The same properties that cause it to clump do the same thing inside their bodies, and since their intestines are so tiny at that age, just a little bit of clumping litter will attract other clumping litter to stick to it, and it doesn't take much to clog up their intenstines and they can die from that.
The clay litter, since it doesn't clump, passes right through them. That's why it's best to use clay litter until they are old enough that they are not playing and/or ingesting litter, and are a little bigger so a few tiny pieces wouldn't block them. When my kittens left at about 9 1/2 to 10 weeks, they were still on clay. I put Rocky on the clumping by 3 months, but I also watched to make sure he wasn't playing in the litter and was having no problem wiht the litterbox. When it's time, just keep and eye and use your judgment as when it's okay to change over. So tell your boyfriend this is only temporary and this is why.
Because I agree, it's much more convenient to use non-clumping down the road.
I wouldn't leave the cat food in the fridge more than a day or two. If you are going to give it to him again, put it in a bowl and add a bit of water and heat it in the microwave for a few seconds, until it's tepid, not hot. Personally, I throw it out after two days.
If you have dry kitten food moisten it with water at this point, or some kmr. When he's about 6 weeks old, that's when his little teeth are ready for the dry kitten food without the water.
You might find it more convenient to have separate bowls for food and water, especially if you're going to be feeding him in spurts, and reheating, etc.
Also, using plastic bowls is not really recommended. They retain bacteria and cats can get sores around their mouths from it. (I had that problem with Deja Vu, and it doesn't matter how often you wash them). Doesn't have to be expensive. Again, I've gotten glass, porcelain oir stainless steel bowls at the dollar store -- nice ones there if you look where the dishes are, not where the cat stuff is. In fact, the dollar stores chain near here sells two heavy littler glass bowls for $1,00 that were absolutely perfect in size and shape.
And that's the only place I buy their toys (exept for a rare special one I might see). Especially since they lose them so much.
Great free cat toy -- the plastic rings that you pull off when you open milk.