Hey guys, total noob when it comes to tire size things so bear with me...haha

I just bought a 09 JK. Came with the 17 inch rims.

After I burn through the stock tires on the Jeep, I want my next set of tires to be some Cooper Discoverer STT 33x12.50 17R

Question is...will those fit the stock rims? I know the 17R of course matches up...but I have no idea how width works with the stock rims.

Also...Question about the spare...will it fit on the back of the Jeep? Or will i need to purchase a spacer for it so it can hang? (Link what I need should I need it)

Lastly, Third brake light...will that be in the way for a 33" tire? (Link what I need to adjust the light should I need it)

Thanks for any/all help!

Edit: May very well go with 285/70/17. From what I can see...they are basically the same size in diameter and circumference...but just not as wide.

If someone could still advise about the third tail light (if a mod is needed) and if i need a spacer thinger for the spare if it does indeed need the extra clearance.