I'm not sure if this makes a difference on how far you can cast, but does a thinner diameter or thicker diameter line makes a spool spin faster & be able to cast farther?

Or will a lower mono line weight, say 10 lbs cast farther than 15 lb, or vice versa on a baitcast reel?  

How does Line diameter affect casting distance when braided line is used???

First figure out what the line reccomendations are for that baitcasting rod(listed on the rod).  Then if you are fishing mono get a mono diameter that matches.  The same goes with braid however the braid diameter is normally far less than the lb rating.  

For example on my St. Croix rods, which are premiers and avids, I have 40-50 lb test because the line diameter is equal to 10-12 lb test.  If I use Yozuri hybrid then I will use the 8-12 lb test which I have in stock.  

But generally lower lb test will cast a little farther.

I'm not sure if this makes a difference on how far you can cast, but does a thinner diameter or thicker diameter line makes a spool spin faster & be able to cast farther?

Or will a lower mono line weight, say 10 lbs cast farther than 15 lb, or vice versa on a baitcast reel?

How does Line diameter affect casting distance when braided line is used???

Larger diameter mono equals less volume of line on said spool. Less volume of line equals less weight. Less weight around the spool equals faster spool startup. Faster spool start up gives you a farther cast.

Braided line will work the same way, but on a much smaller scale. Braided line is smaller, therefore it will pack on the spool tighter. Tighter packed line equals more volume. More volume equals more weight. You have to get into the 30-40lb plus braid to get the same effects as the 10-15lb test mono.

Line memory and/or line limpness have much more effect on casting distance than the spool start up speeds from the line weight. Braid will cast farther than a lot of mono's and floro's becouse of the limpness of it.