no, a neighbor can't plant over a property line, if he or she goes over the line it isn't there property to plant on.
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.
You can clip and trim the trees and bushes on your side of the property line. You cannot go in your neighbors yard. Make sure you know where the property line is by locating pins or having it surveyed.
An encroachment is an infringement on someone else's rights or intrusion on another person's property. It is most often used when describing real property such as the corner of an neighbor's garage that extends over the property line or a driveway that gradually grew over the property line and is now partly on your neighbor's land. Encroachments are often caused by surveyor error in placing the pins marking the boundaries in a subdivision and the party who built their swimming pool partly on their neighbor's land was not at fault.
If its on his property line and there is no easement then the only thing you can do about it is flip him the bird when he drives by.
At common law and in most jurisdictions you have the right to trim any branches that overhang your property. However, it must be done in such a way as to prevent any damage to the trees or shrubs. You should discuss it with your neighbor first.
You are responsible, but your homeowner insurance should cover damage.
In most states, you have the right to cut any limbs or branches that hang over the property line. However, it is always best to work with your neighbor about the tree whenever possible (since you have to live next to that person). If your neighbor objects to you cutting limbs that hang over the line, be sure to see a real estate attorney before cutting to avoid violating your state's timber trespass laws.
With your neighbor's consent would be nice, otherwise you're trespassing and the neighbor could take action that could kill the trees. It's always best to put plantings in so that even when they grow they don't "encroach" over property lines, unless the neighbor agrees.
Depends if the fence line IS the property division line, in which case both homeowners have to agree about the trimming. If whatever needs trimming is solely on your property you are allowed to do whatever it is you need to do, providing any homeowner association (if they exist) has rules for this.
It does not matter what state your in. No one is liable for an act of nature. Your neighbor is responsible for the portion on their property and you are responsible for the portion on your own property.
It sounds like you have a strong adverse possession/mutual acquiescence claim to the fence as the property line. You need to contact a real estate attorney immediately to preserve your right to keep the fence line as the property line. Also see the Related Questions below.
The property still belongs to you. The easement means that you shouldn't be planting or putting anything permanent in there, as the city/town/community could come along and do what they wanted with it.