Perhaps you should clarify what your trying to do. Is it: you have a wireless LAN at your house but your neighbor is interfering with it? or are you trying to use your neighbors network. One would assume you mean boost as "boot" your signal doesn't make much sense, unless your saying you have an AP or wireless router that won't boot. Hopefully your NOT trying to use your neighbors gear and if you are, hopefully nobody here will help you. We'll see I guess. What specifically are you trying to accomplish?
Yeah, your using his gear if your associating, or attempting to associate to his AP. So you call it sharing. That would imply he/she knowingly allows you to use his wireless LAN. Is that correct? or is this just something you would like to do, use someone elses paid service without paying? That would be stealing and this thread should be dead if that is the case.
Your first link is for a bridge. That wouldn't broaden your cell coverage. A bridge would be used if you wanted to use wired clients on your end. The range extender is just a repeater. You could use that if you had a good place to put it, presumably somewhere as close to the middle of the desired link as possible, though it would also be effective closer to the remote side, assuming it was still able to achieve a solid link back to the parent AP. By the way, unless the provider allows this it's a still a minimum, unethical and at most, illegal. I'd read the fine print of the broadband contract very carefully.
And I'd imagine it does make a difference who pays since it's probably not allowed by the provider and the person who has the incoming connection likely would want to be sending in the checks.