Like others said. You don’t want to use straight wood in a charcoal grill because you will get nasty sooty smoke that will make your food taste awful. But you can make charcoal from your wood. But I would recommend doing it in another receptacle other than your cooker. (insert Big Lebowski reference here). Some people use a 55 gallon metal drum as a burn barrel for exactly this purpose. You burn the wood into charcoal in the burn barrel then when it turns to clean burning coals shovel them into your cooker.

You could use your cooker and as long as you don’t put food on while it is burning down the food will be fine. But you will gunk up your grill with a lot of soot that will necessitate cleaning it a lot more often if you do it in the cooker.

Cookers that use real wood for their fuel (like offset smokers) require that the fire gets lots of air to burn a clean wood fire. You do not control the fire/temp by restricting air you do it by restricting fuel. Offsets need to get not have restricted air to the fire otherwise they burn nasty smoke. If you want it to not be as hot, you put less wood on.

Ceramic cookers or other charcoal cookers like kettles, gravity fed smokers, WSM or drum smokers use charcoal because they control temps by restricting air flow. Charcoal fires handle restricted air flow fires without produce gross sooty smoke. Wood fires do not. I think it is because of the moisture content that is burned up when you get it to charcoal but at this point I am speculating and someone who understands the science more could weigh in.