Similarly to qizwiz's question, I'm curious if this could also translate to: "Are they small quantities?" (for example if I can't see the packages/unit size)
Yes, well in that context you could translate either from "Sunt mici cantitățile?" or from "Sunt cantități mici?".
Does "are there small amounts?" have the same meaning? To me it does. I imagine being at a party with a cake and asking this question of the host... indicating I'd like a smaller piece.
I don't think so, there is a slight difference, but not much. Like how you said, it's if asking someone "are the pieces of cake small?" or "are there small amounts?", one is asking if all the pieces are small or if there are any small amounts, which is like saying that you'll take any one that is small. Hope you understood that.
So in Romanian, are there certain adjectives that come before the noun, like size?
It's a matter of context, not of specific adjectives. Here, we have a question and the emphasis falls on "mici". The noun-adjective order switch also takes place in English:
Those are the small quantities. - Acelea sunt cantitățile mici.
Are the quantities small? - Sunt mici cantitățile?
Note that "Sunt cantitățile mici?" is also a valid question, but, for me, it has a different nuance and I don't feel qualified enough to try to explain.