Generally speaking, yes, if it's going to be seen by the public and if the person is clearly featured and not just part of a crowd. One exception to this is the media, which can generally film or photograph people so long as it's a news story. But check your local state laws to be sure.
The definition of mugshot is a photograph centered on one person's face which is typically made for official purposes, for example one is required on personal photo ids such as a person's passport.
An air photo is an aerial photograph - a photograph taken from the air.
Photo can not be abbreviated because photo is the abbreviation of photograph.
a photo -> une photo a photograph -> une photographie
there is no past tense, just photo or photograph.
PHOTO as in picture/photograph
A contraction of Photograph.
Photo
Phot
photo
The verb of photography is photograph. As in "to photograph something". To be lazy you could also use "photo" as a verb. As in "to photo something".
The root of "photograph" comes from the Greek words "phos" meaning light and "graphé" meaning drawing or writing. So, "photograph" essentially means drawing with light.