lol, I see what you did there
But that proves the point exactly... Russian people don't have to think about all this grammar, they just know it instinctively. But even native Russians make Russian grammar mistakes sometimes!
As for learning cases, it can help by translating it from English -> Runglish -> Russian.
Example:
"I want to help you" -> "I want to help to you" -> "я хочу помочь вам"
or
"I have no pets" -> "of me there is none of pets" -> "у меня нет домашних животных"