VA in = VA out. But please note that there are ironlosses ( eddycurrents and hysteresis losses in the iron core )and copperlosses from the windings to be added to the primary power absorbed from the mains. the copperlosses increase with the load I²R, the ironlosses remain almost constant

Transformers are normally rated in VA's. At UPF power factor you can call it Watts but generally its lagging at around 0.95 PF hence VA's are used.

Winding ratios are:
Up*Ns = Us*Np where:
U is voltage, N is winding turns, p is primary winding, s is secondary winding.

Current ratio's Ip*Up = Is*Us. In your case
Ip*120 = 3*12 » Ip = 36/120 = 0.3 Amps.

Personally I don't like to rely on the resistance values measured across the primary or secondary windings because of the different gauges of wires used and the transformer is an AC device. It's Ok to identify a primary or secondary winding.

By unknown transformers, to test I usually put a 200 Watts lightbulb in series during testing which will absorb the fault current if it was accidently the wrong primary voltage. In NZ we have 230 V. and there are a lot of trannys out here with 2 * 115 volts primary windings.

I hope this explanation may help out a little.

The product of rotation, excitation and flux produces electricty.