"...is the hood supposed to feel flimsy at the grill?"
Yes, or at least mine does - almost a side to side twist. It's made to be light
Re motor mounts & shifting, I've never noticed any particular vibration in mine. 1st/2nd shifting can be a bit jerky, but I always put it down to shifting at 5K rpm or so when I pull out from my side road into the busy 60 mph highway.