Trail braking does work, and MR cars do get tail happy under brake, so yes. In fact, get a stock Integra type r, and put super soft racing tires. I remember I did a complete 180 the first time I tried braking into a turn.
So yes, there is weight transfer.
As for engine braking, in the formula 1 cars, the wheels lock up in first gear if you let off the gas, so yes, there is engine braking too.