Dan Hiebert

The top photo shows there is no retaining ring on the shaft to hold the handle onto the housing.  To me that means the handle part may not be original.  If a previous owner thought that maybe the trunk handles or shafts between Plymouth and Dodge were interchangeable, then the shaft is indeed too short.  Personally discovered this myself many years ago.  So, what you're missing may be the correct handle, or at least the correct length shaft.

The latch on the door post is adjustable. 

Yes, the cooling systems in our cars are pressureless.  But pressureless means they don't use pressure to raise the heat range of the system, it doesn't mean they won't take any pressure.  Either way, filling with water, or with air while under water, works.  Not as much equipment needed to fill with water, but you need a keen eye, and you can still miss tiny holes.  Filling with air takes a tub of some sort, and as andyd notes, some fittings to seal up the inlet and outlet.  I had a couple radiators checked at a local shop recently, they used some of those rubber freeze plugs with the bolt that tightens to seal the inlet, outlet, and filler neck.  Then they ran air at low PSI into the overflow tube.  Not sure how much PSI they used, but the systems in our cars can handle 4 PSI just from expansion of the coolant.  Readily and quickly apparent where the leaks are via that method.  

Some call the panel(s) I'm talking about "gravel shields", but I've always called them valance panels, even though Dodge called them stone deflectors.  I'll go with stone deflectors here.  They're the panels that fill the gap between the bumper and body/grill.  The panel that fills the space between the bottom of the radiator and grill is the "radiator front dust shield".  There is a "lower radiator crossbar" that goes between the lower inner corners at the front of fenders.  For reference, the front of the dust shield attaches to that crossbar.  The lower rear of the grill is also attached to the front of that crossbar, you have to access the nuts from under the car, at the rear of the crossbar.  They're kind of a PIA to get to because they're in the bottom of that u-channel that the crossbar is made from.  The stone deflector is attached to the bottom of the grill from underneath as noted above.  The brackets at the bottom of the grill accommodate the screw holes for the stone deflectors, as well as the studs that mount to the crossbar.  So, to sum it up, there are two rows where the bottom of the grill attaches to the car, from underneath through the stone deflectors, and from the rear through that crossbar.  It took me a bit to get my head around that when I took my grill off the first time, then a while to remember that when I did it the second time - both many years ago.
 

The two knobs either side of the Dodge emblem below the speaker - the one on the left turns on the dash lights, off / low / high.  The one on the right turns on the map light that is behind that emblem.

That has come up a few times, it's as PA noted, the dimmer switch for the dash lights.

This is for '46-'48 Dodge but should still apply to your car.  The over center spring attaches directly into that groove.  The spring tension holds it in place.  If it won't stay, it's not adjusted right.

However you get it out of the car, it is indeed easier to work on the whole assembly on your bench.  The steering shaft is not inseparable from the steering box (housing), regardless of what you were told.  And it is not hard to either remove or install it, just takes some doing.  Pull the pitman arm off, because the sector shaft to which the pitman arm is attached has to be removed through the top of the housing, and the sector shaft has to be removed before the steering shaft will come out.  Remove the sector shaft adjusting screw lock nut, and lock washer, those will be in the middle of the top cover.  Remove the top cover.  You can now remove the sector shaft out through the top of the housing.  Remove the bottom cover.  It has a tube attached to it that runs up into the steering shaft.  That is to keep the lubricant in the housing.  There will be a spring, an oil seal, a thrust bearing cup (I was taught it is a "bearing race"), and the bearing that will come out with it.  The steering worm gear and shaft (one unit) will then come out the bottom of the housing.
 
This is interesting, kindly keep us informed on how you get this electric PS installed.  Unknown what you have to do to the steering shaft, but if you have to weld something on to it that increases it's effective diameter, it should not be removed from the steering housing, as you'll never get it back in if you do.  There is not much wiggle room, measure where needed.