Rather then try to answer the specific questions you have asked. I'd rather share my own ideas on them, with the thought in mind that you will have to eventually develop a process that you are comfortable with. That being the case here goes:
"Do most people scan at the original size of the neg at a high dpi" Scanning the full size of the negative, or print/document, insures you you recording all the image elements. Rather you opt to retain the full image, or do selective cropping is a matter you alone can decide. Quite often I end up doing a certain amount of cropping for no other reason then I wear eyeglasses and quite often will have problems with edges in the viewfinder.
As to scanning at a high dpi; This is a little trickier in that I am shooting 35mm so that the resulting file size of the neg or slide scanned at 4000ppi on my Nikon is only going to be in the range of 45/55Megs. You obviously are dealing with much larger files and will have to consider issues of storage capacity and your Computers ability to handle the files. Having said that, and assuming there aren't the aforesaid issues: I would scan the Negs in the highest resolution my scanner affords - because so far as I know that is the best way to pull the maximum picture detail out of the scan.
"do they use around 350 dpi at the size they intend to print" I would not! I have seen recommendations for Inkjet printing at 240dpi all the way up to 360dpi, so why limit yourself to 350. IMHO, far better to scan a Master Image, and then depending on how, or where you print it, or what you want to use it for - do a Save As and rename the file, and then resize that file to what you need it for. That's my own particular philosophy.
I am not going to comment on your last question for a couple of reasons. First of all, I honestly don't know if it does, and secondly; I think you have to decide that depending on your own approach to digitizing and using your images.
Best of luck with what you are doing!