A: This is why it is so important to have your own real estate lawyer represent you in a transaction. You will now need one to review your closing documents, the HOA documents, your survey of your property and the neighborhood plat, which often attached to the HOA documents but not always. The HOA documents and the plat are public record and owners are deemed to have constructive notice of their contents by virtue of accepting a deed in a HOA community.
The seller has the duty to provide you with a disclosure summary which states in part "THERE HAVE BEEN OR WILL BE RECORDED RESTRICTIVE COVENANTS GOVERNING THE USE AND OCCUPANCY OF PROPERTIES IN THIS COMMUNITY." A buyer has three (3) days to cancel a purchase agreement if the disclosure summary is not provided but must do so before the closing.
We cannot review your documents in this online forum but based on your statement of the facts it is likely the private roadway is legitimate.
A: The HOA can contract for bulk cable services and each owner is billed their share of the expense. Usually these contracts have an opt-out for those owners who do not want to use the services. You would need to get more information and take that and a copy of your HOA documents to a HOA lawyer to review and advise you.
A: You have a case for trespass and for damages for the value of the lumber. The issue of your property being landlocked is probably not important to the case other than to provide evidence the neighbor was the one who had access to the property.