A Question on electromagnetic inductance

When we magnetize an electromagnetic coil, it is often that we magnetize more than the electromagnetic coil itself. If we magnetize an electromagnetic coil nearby some iron sheets, theoretically we also require extra electrical energy to magnetize those iron sheets. In a sense, all ferromagnetic material in the universe would have to be magnetize, therefore it should be impossible to magnetize any electromagnetic coil. How could we magnetize any electromagnetic coil? Another question is, does the presence of iron not attached to the coil increase or decrease the inductance of the electromagnetic coil? If it increase the inductance then it would take longer for the electromagnetic coil to magnetize; if it decrease the inductance then it would take shorter time for the electromagnetic coil to be magnetize. So does it take longer or shorter with the presence of ferromagnetic materials? How does the presence of ferromagnetic material in surrounding environment increase/decrease the inductance of the electromagnetic coil?