经常,常 and 常常 mean "often". Chinese words are sometimes doubled to emphasize the meaning, like 谢(to give thanks) doubled to 谢谢 means "thank you". 一点点 compared to 一点 means "an extreme small amount" .
你要不要加牛奶?-do you want to add milk?
我只想一点点- I just want a little bit.
you can think of 常常 as "[very] often" 常常 compared to 常 emphasizes how frequent an action takes place. 我常常和我朋友去图书馆- I often go to the library with my friend. (this is almost like a daily routine)
平时 means "normally" and 平常 means "usually".
As for 通常, according to my Chinese friend, it means "generally." Many of these are not that different from each other, just small but subtle differences.