Help with Hawk 250 bike?

[Pyramid]

I’m new here and new to owning a bike in general. I have been trying to learn, and started off with buying this from a friend who bought this from Facebook. Right off the bat there were a lot of problems I needed to fix but I’m currently stumped on this problem. So, my electrical work stopped working about a month ago. I’m not sure why it stopped, but from posts I have seen on this forum said it could be the starter relay so I went and purchased a new one. I replaced it today, and nothing seems to have changed. When I turn my key my neutral light still doesn’t turn on, and my lights don’t work unless I kick start it. I did notice that a a wire is hanging off near the battery and I’m not fully sure where it’s supposed to hook up too. Could that be the problem or am I doing something wrong? I’m going to try to post some photos with this as well and hope someone here can help me.