Accidently ? - If not very much, it'll probably just burn off without doing any damage. - But be careful in future, cars are not tolerant of most 'accidents'.
your gas tank
Your car will run (poorly) during that tank of gas and it will smoke like crazy while the transmission fluid goes through the engine. Secondarily, the transmission fluid (being very high in detergents and cleaners) will clean your injectors and top end of your cylinders quite nicely. Not a recommended way to clean them, but if you get it in there accidentally that will be the silver lining.
SO far nothing... it's only been about 1/20 of the fuel tank so I'm not sure of the outcome
You'd need to drop your fuel tank and drain it out.
Yes
Depending on what, you may have to remove the tank to clean it, you may have to replace the motor if it is run.
OXYGEN.
NOTHING
The automatic transmission filter is in the transmission. It has an internal filter just like it has an internal gas filter in the gas tank.
remove straps fuel lines and drop tank if its metal take some buratic acid and pour in the tank and if its real bad take a 2ft or so peice of chain and put in tank and shake it around. if its and older model you can run a little transmission fluid through by pouring in the tank before you try dropping the tank, it will make it smoke a little but the trans fluid will instick parts in 94 or earlier vehicles
It will Probably EXPLODE!!
You could have accidentally put in some bad gas. You could also have gotten water in your gas tank. There are many other reasons it could be having this problem including a transmission that could be going out.