transformers work mainly by creating eddy currents in the metal core between the coils of wire.
No they do not! Eddy currents in the core represent loss and you want to minimise them as much as possible. That's why transformers have cores made of a stack of laminations instead of a solid chunk of iron. The laminations are oriented with their minimum-area cross section perpendicular to the magnetic field to minimise the area available for eddy currents to circulate in. The higher the frequency the smaller the area needs to be, so as the design frequency rises first thinner laminations are used, then powdered iron, and then non-conductive magnetic materials like ferrite.
Even before traction electronics it was relatively easy to provide DC and AC capability by feeding a basically DC design from a transformer, and to provide multiple voltages at the same frequency via separate tappings on a trainformer. But would a loco equipped for two AC frequencies have had to have two separate transformers in the past, and if so is this still the case today? As the transformer is one of the largest items in an electric loco then having two would have been a big weight and cost penalty.
The size of a transformer core is determined by the need to avoid magnetic saturation. All else being equal, the flux in the core is inversely proportional to the operating frequency, so the lower the frequency, the larger the core has to be to handle the flux without saturating. A transformer designed for 16.67Hz will therefore be three times the size of an equivalent transformer designed for 50Hz. It can still be used at 50Hz, despite being overlarge - the other way round of course does not work. If you're specifically designing it for both frequencies then the overall size of the core will be as for 16.67Hz, and the thickness of the laminations (see above) will be as for 50Hz. But you perfectly well can do this, and you don't need two separate transformers.
The amount of heat produced depends on the impedance multiplied the square of the current. Keeping the voltage the same, if you halve the impedance the current will double so the amount of heat will also double (half multiplied by two squared).
The impedance of a transformer has two components: resistive, which depends on the length and thickness of the wire, and inductive, which depends on the inductance and the operating frequency. The heat produced in the windings depends on the
resistive component multiplied by current squared.
The resistive component is made as small as possible; ideally it would be 0. The inductive component is zero at DC. So if a transformer is connected to a DC voltage source, the current is determined only by the very small resistive impedance; it is accordingly very large, and something goes bang, hopefully just the circuit breaker but you never know...
If a transformer, with no load on it, is connected to an AC voltage source of the appropriate frequency, the inductive component is much larger than the resistive component, so it is almost entirely the inductive component which determines the current and the current is small. The heat generated in the primary is the square of this small current multiplied by the resistive impedance.
As (resistive) load is applied to the transformer secondary, it appears as a resistive impedance, with a value of the load resistance multiplied by the turns ratio, in parallel with the unloaded primary impedance. The transformer therefore draws from the supply an additional current equal to the secondary current divided by the turns ratio. The heat generated in the primary is the square of the sum of this current and the essentially constant no-load current, multiplied by the resistive component of the primary impedance; heat is also generated in the secondary, according to the square of the secondary current multiplied by the resistive component of the secondary impedance.
