1. Yes, the material must be ferromagnetic. In practice, it means steel (mild steel, more specifically). Other ferromagnetic materials exist, but are harder to obtain. Mild steel, on the other hand, is very common - nails, bolts and many other things. Generally, lower the carbon content in the steel, better its magnetic permeability. Pure iron (like 99.95% pure) would be very good, but you won't find it. Most steel will have like 0.2% carbon or more... Some specifically made alloys can also have very good magnetic properties - like electrical steel (silicon steel). You can find this inside transformers, but you might be disappointed because you will find it in form of thin sheets.
Better material (higher magnetic permeability) can make better electromagnets, but it only pays so much to obtain it. It won't have superpowers.
You can easily check if a material is ferromagnetic - if a magnet sticks to it it is ferromagnetic and will make an electromagnet. (Brass, copper, bronze, aluminum, and most stainless steel are NOT ferromagnetic).
2. Yes, you can wrap wire around any ferromagnetic material and it will show some magnetic effect. You might be disappointed with the oven pan - as it will make a weak electromagnet. If you make a thin and wide plate and wrap a wire around its perimeter, the effect will be small. Magnetic field lines must close themselves, and if your plate is wide they must go long way all around the plate to the other side - if you force magnetic field lines to 'travel' long way through the air it is hard to make them strong (dense, actually). The magnetic field is the 'happiest' if it can travel through iron most of the time and only make short jumps over the air.
A better design would be if you make many small electromagnets (wire around a short bolt) and arrange them side-by-side in a plane to make a plate. You must orientate every other one into the opposite magnetic direction. Magnetic filed lines will 'run' through them from one side to the other side of the plate, taking only short jumps over the air.
3. In addition to the magnetic permeability of the ferromagnetic material, and in addition to the length the magnetic field lines must travel (as said, especially critical is how far they travel through air or other non-ferromagnetic paths), the strength of the electromagnet will be governed by ampere-turns. That is, current in the wire current multiplied by the number of the wire turns.
You can choose appropriate wire gauge to adjust the electromagnet to your battery. With thinner wire you will be able to make more wire turns and its resistance will be greater. The current will be smaller (when connected to the battery of some voltage) and the battery will last longer.
Of course, a wire can take only so much current so there are limits. Another limit is the ferromangetic material itself - it will only 'allow' magnetic field up to certain strength (in practice, some 1.5 tesla - but you will have hard time to reach even this).
All said above is for simple case of DC powered electromagnets (battery). For AC powered electromagnets (or electromagnets where activation/deactivation time is critical), things get more complicated.