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He USAF has fill in roles. JTAC for airstrikes, Combat controllers, PJ's, what have you. Security Forces are often times employed to relieve infantry roles in tasks such as convoy duty and such. But no, the Air Force and Navy do not have infantry, as we are not a ground force.
Yes. The Air Force does have a type of "Infantry". Unlike other branches of the military though these jobs are very specific to the Air Force mission. I cannot answer fully your second question because of my lack of familiarity with snipers in the Air Force. See this for a type of job that the Air Force would have for you. --> http://www.airforce.com/careers/detail/combat-control-males-only/