[Sumippi]

I think 「きのうほんをよみましたか。」is grammatically perfect.

「きのうたべましたか。」sounds unnatural. If you say this, it'll sound to me like you're saying I didn't eat anything at all yesterday-- and I think maybe you can add an 'object' here, like 「きのう、なにかたべましたか。」(Did you eat anything yesterday?) , which would make its meaning clearer.
Or maybe in a colloquial use, when the asker and the hearer already know what food they're talking about, then I think 「○○を」,「あれを」or「それを」can be implied so you can say 「きのう、たべましたか？」.

「きのうしましたか」also sounds unnatural to me and here again I think you should add an 'object', like きのうテニスをしましたか？(Did you play tennis yesterday?)　because する is usually used with an object, like when you say 'play games' 'play catch' 'play a role' 'play a trick' etc.
So 'to play' without an object, as in 'Did you play yesterday?' would be translated 「あそぶ」, not 「する」.