"Chewed pencils are of the devil. >_>, Not bad, pretty impressive. Here are just a few additional notes for ya. Before I give you these notes sit at that randomn table I gave ya and say hi and date this lit candle sitting across from you. Her name is Aqua....don't ask why but she wants to be called that >_>, get her number, give her the googly eyes,but don't piss her off....tis will help you understand fire ^^......it really will...believe me. LOL
One thing to note about fire is that it can be used anywhere anytime. It is extremely useful in that sense, as unlike Earth and Water you are the source of the flames, or you can seemingly channel this chakra into other areas around you. It is mainly used for offensive purposes and has very little versatility outside of that, but for me that is enough as it is so destructive and deadly it more than makes up for its lack of versatility (as in defensive or supplementary use). Another thing about fire is that if it is large enough it will block your vision from whatever is infront of it so you must be careful when using some of its larger techs, or even if you use small techniques.
Fire can be combined with all elements in a useful manner. That's right even water.
Fire when combined with wind in the same direction obviously gains strength (its worthy to note that you must remember what is getting powered up, what is the medium of attack. The wind goes into the fire so it is your fire that ranks up, not the wind)
Fire can be combined with various earth jutsus to create lava based attacks. You can see here it has created another element instead of a simple powerup to a basic element.
Fire when combined with thunder cover each others weaknesses. Lightning is now protected from wind jutsu's and water jutsus will come in contact with Raiton. Neither element is a medium because they are both intangible and pass through each other. You can take advantage of that fact and keep pressure on the enemy.
When combined with water they cancel each other out if the proper ranks are applied, even then the fire coming in contact with the water will create a makeshift steam that can help hide you from an opponent or blind them to your strategies. Can also be useful for genjutsu usage.
I don't have much to say for KG and weaknesses as you did pretty good, here are some other important KG
Fire is neutral to Wood contrary to what an intuition might have you believe. LOL
In regards to shadows Fire can be used to create shadows or eliminate them. It all depends on how it is used.
Fire can is strong to the clay variation of Blast release as you can melt clay or cook the clay to weaken/and harden it.
Fire is also weak to Dark Release.
Fire is weak to Dust
Dead Bone Pulse is weak to high levels of temperature. It is also known as Shikotsumyaku
Konans paper is worthy to not being neutral to Fire as that goes against most intuition.
Any questions before me move on? If not continue your date as I prepare some exercises to build that Katon chakra. ^^"