Drawing air in through the keyboard = drawing all the crap in through the keyboard that falls on top of it (getting it under the keys, etc.). Never mind the air flow restriction causing the fan to have to ramp harder.
No, most notebooks don't. In fact, I've never heard of such a design. Keyboards have a backplane, so air wouldn't pass through the keyboard assembly anyway.
Most notebooks have an intake vent directly above the fan.
Yep, any high performance notebook will generally have air intakes on the bottom/sides. In fact macs are quite sparse when it comes to air intakes, most windows workstations have air intakes all across the bottom panel below the fans.