Yes.

If the specific frequency is not clearly marked next to the impedance value on a data sheet check elsewhere on either the data sheet, application notes or general information or on another data sheet (as the data sheet you are looking at may be a short form version missing some information). If it's a data cable it will be there somewhere.

If the cable is not a data cable then the information will probably be located in a general cable or application note. Try the cable website for more information.

Not necessarily. If the impedance specified is the "characteristic impedance=Zo" of the cable, that is

Zo=sqrt(L/C)

Where L is the cable inductance per unit length and C is the cable capacitance per unit length. Both of these are dependent only the physical size and spacing of the conductors and the insulation materials used in the cable.