attraction force on electromagnets

The answer to the second question is yes, provided the N and S poles of a given magnet are shaped the same way.

The answer to the first question is not as simple as you would hope. It depends one whether the magnet is a horseshoe magnet, a bar magnet, a solenoid, a toroid, whether there's a ferric core,...

PD

As a personally interesting anecdote, I was once responsible for the design, construction, and operation of a 250,000 lb iron-core toroidal magnet. I chose to instrument it with a Hall probe, embedded in a thin slot in one side. But the slot itself would disturb the field, which I had to account for. I proposed a linear model to calculate that, superimposing a piece of "negative iron" where the slot was, and calculating the total field of the magnet, against which I could compare the Hall probe measurement. This approach was deemed clever by my professors until a young post-doc pointed out to me, in a fatherly conversation in the hallway, that iron core magnets are nonlinear beasts and superposition doesn't work, a revelation that left me sick to my stomach. Sure enough, the Hall probe read values that were inconsistent with calculations and with the backup instrumentation. I ended up doing a very complicated lattice-relaxation calculation on a mainframe computer to compute the field.

PD