The consensus seems to be that the effective range for a .243 is 400 yards.
(I don't have one so I couldn't say for sure).
The bullet weight and composition and the powder charge propelling it are going to be a factor.
I wouldn't recommend it for anything more then varmints at that range.
About 900 yards
Out to 1000 meters or so.
you should pay about 300 to about 350 dollars for a Remington 243 rifle
Depends on if that model is offered in 243
Because that's what the bore measured out to.
Great rifle.
50-400 usd
A 223 would be fine for a deer rifle but you need to make sure the (youth) person can hit the kill zone. I would suggest the 243.
Varmits to deer.
The .243. It's basically a necked down .308 Winchester.
That depends on the exact model of rifle.
Only if he has a powerful rifle and is shooting from a safe distance.