Hello, I am a solicitor with 20 years experience I will try to help you with this.
1: No it does not.
2: It probably means the physically adjacent land, unless there is something about the context and location or the covenant itself that would make it mean more. "Neighbour" is an imprecise word which really should have no place in a covenant of this nature. The covenant should identify the land that benefits and those should be the people you contact. It is probably wise to err on the side of caution.
3: I don't see why they cannot charge for giving consent.