Possible that i might get skin cancer on my arms and legs if already on my face?

Yes: If ou have fair skin and significant sun exposure you should have whole body screening including arms, legs, trunk, feet and scalp. Typically basl cell carcinomas are the most common, but if you have one or more kin cancers on your face you should have check up a minimum of once a year.

Yes: Yes, but the relative frequency depends on type of skin cancer and your own skin type and sun exposure. Melanomas can occur anywhere. Squamous and basal cancers are much more likely in sun-exposed areas, like the face, scalp, back of arms, etc. If you have had a skin cancer - you should be checked from time to time by your dermatologist or primary doctor.

Very possible: Skin cancer is due to sun exposure. The head and neck is very common, as are the exposed areas of the arms, hands and legs. If you have any concerning lesions seek evaluation soon. Otherwise, just keep the surveillance appointments your dermatologist has likely scheduled for you.