first, do you need good math skills to be a nurse? how much math do you usually use and on what level?
yes, you need good math skills. that doesn't mean you have to be "good in math." most nursing schools require either elementary algebra or college algebra. you can look up some course descriptions of each to get an idea of what they cover. you won't use everything you learn in the class but it is important in training your brain. bsn's also usually require statistics. the important thing about statistics after you leave the class, imho, is not that you can do all the math involved but that you understand what research projects show when they use statistics in their reports. in the day to day job of nursing, there isn't usually very much math but it is essential to be rock solid in what there is. the doctors orders aren't necessarily given in the same units that the medicine is available in.
second, i've read that a lot of paperwork is involved. what kinds of things are on the paperwork?
a nurse needs to record measurements and observations, and what was done for the patient and when it was done. also, plans for what should be done later (or what changes should be made in what is being done). these things are done via charts (literally, like on graph paper), or forms that list what is usually measured/observed/done and the nurse puts a check or number there, and anywhere from a few lines to a few paragraphs of information at a time. unless the nurse is working in education or research, i don't know about community service. that these things are sometimes done on a computer instead of actual paper is irrelevent to what is done.
lastly, what is your day usually like? what do you do? what kinds of things need to get done before you leave? it's it like a routine you get better at each day?
i'm not a nurse yet but from shadowing and volunteering in a variety of placess, and researching it, i'd say it varies tremendously depending on the kind of nursing and varies somewhat on the particular employer within that kind of nursing.