Hey yourfateissealed,
You always could sit on the staircase and there do the Websurfing
.
By good chance you could even look in guts of your neighbours machine.
At the same time your neighbour, by good chance, could look at your private stuff.
Nothing to it, if it is an unsecured Network.
Now to get to real terms, I have a secure Network, but occasionally get an unknown Wireless MAC Address listed on my Router. (Was connected, but not getting past my Router). So I know there was somebody (neighbour, drive-by, worm) that was trying to get a free ride. I rely on the settings of my Router to block that MAC and dump it by restarting the router.
In my case the ISP service cost > $30 per month. I would not like to share my connection with the neighbours.
To be fair you should talk to your neighbour, and see if you could "share" for a few bucks. After all, he/she is the Owner of that signal.
I am not familiar with repeaters, but I am sure it must first know the "Signalling IP Address" before it will properly will pass the Signal.
If your neighbour declines, your repeater investment will be for nothing.
If your neighbour agrees, he/she must install it. Then you should study-up on "how to secure" your own data.