If I apply the electric and magnetic field separately in two perpendicular directions on a conductor then is it behaves like conductor placed in the electromagnetic field? Is" electromagnetic field "and (electric & magnetic) field acting in the perpendicular directions is the same?
'Electromagnetic field' is a term that describes both the electric and magnetic fields together and also separately. This means that even if you only apply an electric field, or only apply a magnetic field, your conductor is still in an electromagnetic field. And yes, if you apply them both, you would still have an electromagnetic field. This means that, of course, Maxwell's equations would be satisfied, but otherwise, you can do whatever you want with the fields, it is an electromagnetic field in the end.
Also if you are interested in the specific system you have in mind, you might find Hall effect interesting.