You can get a 9 tooth sprocket, you will need a conversion kit to do it. Haro makes a decent one just do a search for Haro 25/9
If the driver/freewheel isn't too badly worn you can keep using it even if you replace the sprocket.
I don't really know what you're calling a driver, but it's probably the sprocket and the freewheel mechanism. And yes, it can be removed. You need a special tool, a freewheel puller, and it has to match the make of the freewheel that you have. check out www.parktool.com for more info.
No. a 9T sprocket will only fit a cassette hub, and not freewheel hubs.
Unless by freewheel you mean driver (in which case 8-9) I haven't ridden bmx in a few years but last time I checked the smallest freewheel you could buy was 12 tooth which would make for quite a low ratio
As far a the sprocket in the front goes, i think they make them as small as 22 tooth, and in the back, it is called a freewheel or a driver. Freewheels are generally larger and drivers are smaller. Drivers can go as small as 8 teeth i beleave.
13t driver goes on a 33t sprocket
well if you have a 8 tooth rear driver you will need a 23t sprocket, if u have a 9 tooth rear driver you will need a 25t sprocket, if u have a 10 tooth rear driver you will need a 28t sprocket, and if you have a 11 tooth rear driver you will need a 30t sprocket
a 25 tooth sprocket will fit on a 9 tooth driver
possibly, if you have the kind of hub where its solid and you can put on a single piece freewheel than no. But if you have the kinde where you need the single piece freewheel and a bolt to hold it on that yes. what you do is spin the thing that holds it on off and screw your nine piece driver it.
9 tooth driver
Front of the engine, points at the driver side cam sprocket.Front of the engine, points at the driver side cam sprocket.
Any size will work. What'll work best depends on what you want it for. Higher top speed - go for a big sprocket. Quicker off the start - go for a smaller sprocket.