Should I ask profs if they're accepting graduate students?

That is usually done. All of my friends including my self (this statement makes me a schizophrenic) have asked professors such questions. Although in many of the cases it does not greatly help your application it is nice to know in advance if there are no other professors you would like to work with. You may include a 1-2 sentence biograph of yourself and sometimes (rarely to mediocore chance) the prof. is interested and asks for more information. In that case that email might also be useful for your application if the Prof is in the selection comitee or knows someone who is.