Honda CRV 2013 vibrates?

My Honda CRV 2013 vibrates a few minutes of start and on acceleration, especially when the aircon is on… Not much or seemingly nothing when the aircon is off. But after some minutes, say 20 minutes, vibration is gone. What may be the cause?
I have changed my transmission fluid and differential fluid.

Does AWD make a huge difference in the snow?

It snows pretty bad here in the Winter, so my girlfriend went to Honda and got a good deal to trade in her old 2017 Chevy Cruze she said she always got stuck in slush and snow even with snow tires on.

She really liked the Civic but the guy said its a FWD vehicle and that she will probably get stuck like the Cruze. Instead he offered the CRV Touring with AWD and 4WD capabilities. She said that when she got stuck she was able to move forward a little bit, but when it came to backing up she was stuck and the Honda guy said its because the rear wheels don't have any power. Hes like with winter tires on the CRV its much safer than a Civic with winter tires.

My girlfriend is a real estate agent so she drives a lot. He was saying that ground clearance matters a lot. There's an AWD TLX but it has low clearance?

2004 Honda CR-V. Weird noise when accelerating?

The noise only happens when I slam on the gas when the car is completely stopped, the noise only lasts for as long as I keep my foot on the pedal, once I let off the noise goes away. If I lightly press the gas it won't make the noise at all. Sometimes when I have a people in the car it'll make the noise even if I have a slow start up. It only makes the noise when I press down hard on the gas pedal when starting to move the car, while driving the car, it doesn't make the noise. I would best describe the noise kinda like a grinding or rubbing, it seems to be only herd up front not rear of the car. 2004 Honda CR-V EX 4wd.