What is the role of 都 in 你网上小店都卖什么东西啊？
都 is an adverb. The subject is 你(的)小店.


  你最近都在做些什么啊？
  你都去过那些地方？
  你平时都听些什么样的歌？
  你都怎么想的？
  ...


When 都 is used, the question sounds less specific. The speaker either expects a long or complete list, or expects the listener to elaborate at length or in detail.