You're right about 國 and 普. 國 comes from 國語, what they call the language in Taiwan, and 普 comes from 普通話, the standard name for Mandarin on the mainland. Not sure about the first reading, though.
If I had to guess about the first reading, I'd say it's the actual reading of the character, and that the other two were just appended when they started using it for 什么 (甚麼). If memory serves me correct it originally (that is, before using it in 什么) meant "ten people," or maybe it was just another way of writing "ten."