It is more correct, and in my opinion more natural, to use "remind about." "Remind me about X" means "help me not to forget X." Thus, your examples #2 and #4 are better. #1 and #3 are OK, though.
Usually, "reminds me of X" means "makes me think of something similar to X." For example, "Her face reminds me of Jennifer Aniston's." In a once-famous commercial, natural-foods guru Euell Gibbons said that the taste of a certain brand of breakfast cereal "reminds me of the taste of wild hickory nuts." He didn't mean "I need to do something so that I don't forget the wild hickory nuts." He meant "the taste of the cereal suddenly brought to mind the taste of wild hickory nuts."