There is no way we can possibly answer this question for you, because you didn't provide enough detail. Do you own the "parkway" itself, or the land it is on? If not, then you don't really have any right to say who can and cannot use it. If it's a public street, and the city allows anyone to park on that public street, then your neighbor can park there. If they allow only residents of certain areas (or people with special stickers) to park on that street, then he can park there if he has a sticker/lives in that area (since he's your neighbor, this is probably the case unless the boundaries of the area are defined in a particularly convoluted way).
Even if you do own the parkway or the land it's on, there may be an "easement" allowing your neighbor to use it whether you like it or not. Making this even more complicated, if you have allowed your neighbor to use it for long enough, you may have CREATED an easement allowing him to continue to use it even if you have since changed your mind.
If you want a definitive answer, you need to talk to a lawyer. Take along all the documentation you have on your property (title deed, etc.).
It is called encroachment. Be sure you know the boundaries of your property before opening a discussion with your neighbor. If you decide to let the neighbor use this portion of the property, be sure to get it in writing you are allowing the use. Without a written document, signed by both parties and notarized, the neighbor could eventually claim the property through adverse possession. Read up on the real estate laws for your area.
I would just ask your neighbor.
Yes, if you are blocking your neighbor's free access or causing any inconvenience. Even if you own the property you own it subject to your neighbor's right to use it. Neither one of you can park on the driveway so as to block the other party.
no
The following information is general in nature. You should consult with an attorney who specializes in real property law in your jurisdiction if the problem cannot be addressed by the following. There are several steps you can take and you should act immediately. You should make certain you know the correct location of your property line and that your property line is clearly marked. You should take some photos showing your neighbor's vehicle parked on your property and make certain the property line is visible in the photos. You should send a friendly, polite, businesslike registered letter along with a photo explaining that the car is parked on your property and request that neighbor not use your property for parking their car. Make certain the letter is to the point and friendly since you may need to use it as evidence later. Request the neighbor stop parking on your property immediately and keep monitoring the situation. If your request is ignored then you should consult with an attorney about taking a stronger position.
You need to be careful that your neighbor doesn't acquire any rights in your property. You should inform the neighbor that he/she is using part of your land and then make the decision to allow the use or not. As long as you acknowledge it and allow it they cannot claim the land by adverse possession and you can ask them to stop using it at any time. You might also record a notice in the land records to prevent any claim of easement or adverse possession over your property by that neighbor. You should seek the advice of an attorney who is familiar with property law in your jurisdiction. You can read more about it in the link below.
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.
Your neighbor has no authority to grant any rights in your property to a third party unless he was granted the right to do so by you or a prior owner of your land.
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.
Unfortunately you don't say where you are because laws vary widely as to miscellaneous property rights such as your question. The first thing to do is ask your neighbor's permission just as a matter of courtesy. Many people assume everything has to have a legal underpinning. There are practicalities here if your neighbor doesn't want to look at a deteriorating wall. Be prepared to offer up your insurance to show your neighbor that if you or contractors go on their property and there's an injury, that the neighbor is protected. You also don't say whether your house is actually on the property line but by the use of the word "adjoin" I will assume so. You might need to check the land maps and zoning for your neighborhood. It is possible when it was laid out there were no "setback lines" requiring your house to be so many feet from the property line (for the very reason you need), or your property was split off a larger tract. Either way, either the subdivision plats and/or the zoning laws of the time, or the chain of title in the deeds for your and your neighbor's property, may disclose that there was a right of easement (a specific right of ingress/egress, etc.) for the purposes you need. Even so you might need to show your neighbor that you have insurance.... Finally, there may be a law or ordinance that allows a landowner the right of reasonable access to a neighbor's property to maintain, but you will have to check the laws and ordinances of your locality. You can do a fair amount of this homework, but if you are still unable to find something specific and can not otherwise obtain your neighbor's consent, or your neighbor refuses, you may have the engage an attorney to research further for you. Good luck!
Yes. The law gives you the right to trim bushes and trees that cross the property line up to the property line. You must use reasonable care in trimming the bushes so that you will not cause damage to the bush (except for removing the parts that cross the property line). If at all possible, talk to your neighbor before trimming.
Generally no. We all throw snow on our neighbor's property after a snowstorm. In some cases it would be impossible to honor property lines especially if your driveway runs right adjacent to your neighbor's lawn area. If they are causing a problem or damage that could be prevented you have the right to ask they stop and find another way to remove snow. Document the damage pr problem cause by dated photos, inform them in writing and ask them clearly to stop. Make sure your letter is friendly, polite and to the point in case you need to seek a court order later on and use it for evidence that you gave the neighbor notice.