Why did he tell Aladdin that he down by one wish even if he didn't wish to get out of the cave even if he forgot he did that on his own? and Why did he think that Aladdin wish to ask to help him save his life from drowning when he rescued him on his own too? Aladdin didn't really make his second wish at all, he just made his first wish to be a prince.
Yes mainly. Genie thought Aladdin wished to get out of the cave because he was tired of it. Genie didn't know Aladdin was actually expressing his questions of trusting Genie. So Genie took Aladdin out of the cave to demonstrate what a genie could do.