That type of issue is handled locally. You need to call your town offices and ask for the building department.
As long as the fence is on your property, no.
The fence cannot be outside your property line.
Yes, if they own the fence.
If the plants are on your property they may be planted along your neighbors fence. However, climbing plants that will grow over the fence cannot be planted along your neighbors fence. Caveat: Make sure your neighbor has not installed the fence "inside" their property line so it lies a short distance FROM the property line. That is the practice in some areas and is required by the city ordinances in some areas. In that case, the land along the fence would belong to your neighbor. You need to determine where the property line is located and not assume the fence is on the property line.
I'd like to install a chain link fence around my property. Are they difficult to install?
Build a fence. It is not uncommon for land owners to fence off their property to keep people or animals out.
when building a wood fence in the town of Brookhaven what side of the fence is supposed to face my neighbors property
You get written permission from the adjourning property to install your fence and attached to theirs.
If the fence is their property, and not yours; you would need their consent to make any modification to it.
If a neighbor wanted to install a fence the fence has to be on the neighbors property entirely. Not half the fence on your side and half on the neighbors side. There are also zoning regulations that deal with issues like this. Some counties will not allow a fence to be over five feet tall and they have to be constructed using only approved materials. I know that in my neighborhood metal fences are against code and they can only be constructed using fence block. If I were you I would call the city planning office and ask them, they will have a definitive answer. Who knows, maybe the fence was put up without the proper permits and your neighbor has to take the entire thing down.
A common fence is a shared boundary structure between two neighboring properties. It is typically built and maintained by both property owners to provide mutual benefit and to mark the separation of their land.
You first have to prove this fence is in fact, on your land and not your neighbors. You do this by obtaining the survey that is filed along with your deed. And then, if there is further questions, you might have to hire a survey company to re survey your property, physically mark the property lines and then give notice to your neighbor that his fence is on your property, justified by a copy of the survey and give him a time frame in which to remove this fence. Then, if it is not done, remove it and sue for the amount it took to remove it. You should read the contract you signed when you purchased the property. Many contracts for the purchase of land will state if an existing fences is the property line regardless of what a survey shows.