Translation:My little sister and I play table tennis every day.
It should actually be "every day" (which is an adverbial phrase describing when something is done). The single word "everyday" is an adjective meaning means "ordinary".
Yeah that's right, "me" is an object whereas "I" is a subject, so it is required to be "I".
Also I'm not sure if this is a grammar rule, but "I" should normally go on the end. [I and my sister] = no, [my sister and I] = yes I'm quite curious as to why Chinese does it the other way around...