What will a motor rated at 1800 watts / 120 Volts draw from the 220-240 side of the 110 V trafo

Edit: Misread question so this doesn't apply to the question asked.

The motor will be 1800w when connected to 120v but roughly 7200w if connected to 240v.

A 230v 1kw heater for simplicity, will have a resistance of around 50 ohms which is what makes it 1kw at 230v. Connect it to 460v and the resistance is still 50 ohms, so double the current flows. Double current double voltage means the 1kw heater is now a 4kw heater. The moral of the story is, a 1kw load is only 1kw when connected to its intended voltage.

I misread the question

As for the losses, its very small in transformers, but the 7.5 amps in will be a bit higher as the motor has a power factor component. It may be around 10 amps if the motor is at full load.

It does of course, hence the OP 7.5 amps calculation being correct.

In addition there are transformer losses. Small as they are. Higher, percentage wise on smaller transformers compared to large power transformers such as used on the distribution network. They are probably above 99% efficient in the transform process.

I'm up that time every morning for some reason. Didn't actually change anything really, just reducing the chance of confusion. Quoting 10 10 10 seemed to need a couple of attempts to work right.

If you connect a 1kw heater rated for 110v to 220v, it will now be a 4kw heater. You have double the current through the same resistance. It can be visualised why, or we can simply say I^2xR which means double current means 4 times the power.