"我不可以买东西“ doesn't sound like a native talk, what did the speaker want to express? If he or she wanted to say:"I cann't buy it (because I forgot my wallet or something else)", it should be: "我买不了东西。" “你买什么东西了吗” means "Did you buy some thing?" Here "什么" doesn't mean "what", it means "some". 你买什么东西了吗? almost equal to 你买东西了吗？

东西 nearly means the same as things, anything, thing. single or PL. 我不可以买东西, I cannot buy anything. it's focused on the willing or awkward situation that you cannot buy. 你买什么东西了吗? Did you buy any things/ anything? focused on whether you bought anything or not, and they intend to know what you have bought.

The first is something you have bought. The Second is something you want to buy.