yes. because of u asking this question chances are u have already hit ur head on the ground pretty hard. to prevent further dammage and stupidity u should most deff where one. but not the cheap ones ither make sure u pick the most expensive one for u are hitting back yard jumps!
no you don't need a full face, but if it makes you comfortable wearing one, by all means. just go to the bike shop and ask the guys there, you'll get a lot better info than a bunch of people laughing at you because you're asking a ridiculous question and you obviously don't know much. at least at the shop they'll be nice to you because they want the business.