"Yes,if just run the 12v lights,is this toyota battery OK?"
It will work if you are not in a position of buying a DEEP CYCLE:(
"I need to buy battery terminals and connect the white wire to battery green(-) and connect the black wire to battery red(+)?"
YES:)
"need make sure white wire follow to convertor and black wire not follow to convertor?"
At this point, don't worry about that, just connect the battery as instructed & see if your lights work, remember the toggle switch, as I mentioned earlier.:D
"if the white and black wire connect to battery,and connect popup to my home plug,will the convertor charge the battery? how long will be full?"
In short, NO, it will not.:(
"I buy a charger,which charger is better? can it charge both toyota battery and deep cycle battery?
Check with your local Auto Parts store & tell them you need a "smart charger" for 6 & 12 volt batteries, then follow the instructions for using the charger.:@
