There are many questions here, so I will try to break this down to basics.
My vampires (all my paranormals in this book) are essentially human with the addition of some genetically amplified senses. Vampires specifically have their vision boosted. This has resulted in the ability to see ripples in the patterns light makes, which for some of them makes them a little psychic (they can see auras) and for some they have a little low-level ESP. This goes into future incidents making changes in the pattern of light, but I don't get into a lot of detail about that in the book. This likely made them a bit -odd- in comparison to regular sorts of people. Humans don't like anyone different as we've so beautifully displayed over our history. It doesn't take very much for us to point fingers and call names. Or more.
In addition to their not so amazing abilities, some of which DO tie into vampire folklore, they are also EXTREMELY sensitive to sunlight. This is kind of a big obvious one since they have that whole extended vision spectrum thing going on. Being out in the daylight very long gives them severe migraines. Exposure to strong lights of any kind does much the same. Most of the light sensitivity starts showing as their eyes really begin to develop, anywhere from birth to five or so. Some of them (in modern times) manage it with medications and other therapies, but most of them just find night jobs. They also have some weird food allergies, which is likely tied into odd genetics. I didn't go into that in this book, but if I expand the series, I'll explore it.
If you do a little researching on vampires you run across some interesting theories about how stories about them began.
During times of plague, fingers were pointed at some particularly unpopular people. Sometimes not so dead bodies were buried. There is more stuff out there, but it made me think quite a bit, and if it made me think, and with hints I dropped in my book, it could make anyone think.
If you had someone living next door to you that never ate any of your fabulous cooking (claiming food allergies) and was weirdly pale, had very odd hours, and was just plain an odd sort of person who was always giving you bizarre warnings about Joe the mailman, or the pizza delivery guy overcharging you, or telling you your hubby was cheating, (or other tweaky and nosey things) then suddenly dead bodies started popping up, who would you blame?
I'm sure you THINK you'd have an open mind. I'm sure you'd try to be kind and neighborly, but wouldn't you wonder?
As far as why they have allowed the rumors to continue, in the beginning it was due to habit, then fear of how humans would react (they are the minority and not at all powerful or magical), and when my story occurs they are mainly at a point where they are all sort of sick of the situation but not sure how to go about coming out of the closet.
For the term vampire, that IS what they are. It is what they were named. Forgive me for using an unsavory example here, but consider the word nigger. People of color did not chose that term. It's absolutely a slur. However even today as many people of all colors try to eliminate it from our vocabularies, African Americans everywhere use it as part of their everyday language in reference to themselves. Is what I have done such a stretch?
If there are any questions I have missed, let me know.