Does a device only draw the current required from a transformer

does a device only draw the current required from a transformer even if the transformer is rated at 12vdc and 500mA when the device uses 12vdc and 300mA?

Im most cases that will be correct.

However small wall warts and other cost conscious consumer transformers are often specified at their rating limits.

This means that the transformer will give a nominal 12VDC when under full load. Under low load the voltage will usually be higher (sometimes quite a lot, 19V are commonly seen no load output) and in some rare cases the higher voltage may cause problems with sensitive equipment that has limited internal voltage regulation.

In your case there is likely to be no problem as the rating is close to what you plan to use and will likely perform fine and operate cooler as it is not near the design limits.

If the device has good internal regulation it will not matter at all as long as it is within the input voltage rating of the regulator components. If the device has a secondary switch-mode supply then the higher voltage is a bonus (it will draw even less current) but max voltage must be within the component limits.

Yes