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UK is 220v
120V appliance will not work on 220V. Use an instrument transformer or voltage regulator to adjust the high voltage to the desired level.
You don't, at least, not legally.
No, 120 v is not enough.
Brazil has a nominal voltage of 220/380V.
You can buy a converter.
If all the components are rated to 220V, yes. Keep in mind that if the appliance was designed for 110V it may arc if 220 is run through it. If you don't know the device can handle 220V, don't run it at 220V. Chances are it was manufactured cleaply and cannot handle the extra voltage.
This type of a transformer is known as a step up transformer.
220 volt will use less energy.
You can surely buy one on eBay, yes.
Is the 220V plug 220V only or 110/220V? (The former will have 3 prongs and the former will have 4) If your case is the latter just use the ground, neutral, and one of the hots. This will give you 120V single phase. If the case is the former you can't get 110V off that plug.
If the motor is designed for 120V or 220V whatever the case, it will function properly.If it is a 12V motor and you supply 120V it will make a mess and you will probably get hurt from flying debris!