The wooshh sound might be normal. It is the brake servo. If it was leaking air you would have known. The brakes would be very hard to operate. I will check with my is250 and let you know if I find it alarming.
No, I am not a mechanic. But I try to get my hands dirty. I had experince of using car motor mounts for some project so I just know that much. Other than, I was once going to change motor mounts on a mazda. They were hydrolic. Easy job but lexus will be quit complicated. Plus if it is the motor mount, you might need to hoist the engine. In case of mazda being simple design, I just lifted the entier engine using a plank of wood and a trolly jack. Thinking about it, it might not be DIY for lexus but you can try visual inspection before any conclusion.
I have seen 4 types of motor mounts. Simple rubber, hydrolic, vaccum based and motor based. I am sure someone will post picture of a diagram soon here. I do not have access to the manual just now.
The exhasut; I noticed on someones car with a bad job that the exhuast was not free hanging and it caused vibration to travel through chasis. But this should not be true in your case.