Can you run a bitcoin lightning node on a raspberry pi zero? Will a bitcoin lightning node run on a raspberry pi zero? Does it have to have the full Bitcoin blockchain synced or can it connect to a remote node? Also what are the minimum requirements to get a lightning node up?
Will a bitcoin lightning node run on a raspberry pi zero?


This probably depends on what you are doing on the node, how much traffic it gets, etc. I have one running on a Raspberry Pi 3B with basically no traffic and its currently utilizing virtually no CPU and 0.8% memory.


  Does it have to have the full Bitcoin blockchain synced or can it
  connect to a remote node?


No, it can connect to a remote node. For example, see https://github.com/ElementsProject/lightning#getting-started.


  Also what are the minimum requirements to get a lightning node up?


I would recommend setting up C-Lighting, it currently works on Linux, and the dependencies are listed in the Installation section. You also need to fund a channel in order to be able to do any transactions.