To answer your first question, yes the intake is under the windshield cowl. Remove the wiper arms, then pop the hood to access three Phillips screws and two push pins that hold the cowl to the cab. There are big holes in the cab for air to flow in. Some trim levels have plastic screens that pop in to provide a rudimentary filter. If you're interested, I have a set. If your truck was originally equipped with A/C, the A/C evaporator in the dash is a big collector of debris since all HVAC air flows through that no matter what the temperature selection.
To access the controls you really need to remove the entire dash. Nothing is sealed, it can all be accessed and serviced, it's just a pain. I wouldn't be surprised if the heater valve under the hood is frozen or or stiff. This puts a large strain on the blue HVAC cable, which might have bent. Also, when stuff stiffens up, sometimes the HVAC control assembly simply cracks. So don't force the levers if they are stiff. A good teardown, clean, and lube can make all the HVAC move like butter and save precious parts from breaking.