Is it a square neck or a round neck? Are you going to play spanish style or lap slide style, if it's a round neck? If it's a Style 1, it's a tricone so it has an aluminium bridge that the bridge saddle insert fits into, and the bridge insert is traditionally hard maple. Sometimes you laminate a piece of ebony onto the top of the maple, but I can't see why you couldn't exchange it for an ebony or rosewood insert, I doubt it will change the tone at all and it's so easy to change that you can easily experiment. Yes, the feet sit on the cones directly. On a metal body instrument the neck angle is usually somewhat adjustable with a neck bar that is shimmed inside the body. Details here:
http://www.strangeguitarworks.com/natio ... eck-reset/
You can first measure the neck relief if it's a round neck, if it's a square neck neck relief is kind of moot. Round neck, look for less than .010" between the neck joint and the nut for reasonably good playing action. Lay a straight edge on the frets and see where it comes to at the bridge - for a round neck, you would like the straight edge to be around 1/8" - 3/16" below the top of the bridge, that will give a standard action height of around 1/16" -3/32" (half of the distance at the bridge) at the 12th fret. If it's a square neck you want the straight edge to be around 1/4" to 3/8" below the top of the bridge, and about equal to the height of the nut above the fretboard. This is where neck angle comes into play. These often have the neck angle "under-set" so the straight edge on the frets comes out way too low at the bridge, this is where you might have to re-shim or adjust the neck angle up. Be wary of adjusting the bridge height too low, you also want to look carefully at the string break angle you get over the bridge to the tail piece - you don't want to go lower than around 4 degrees as the string breaks over the bridge, so you are looking at both sides of the bridge when you are getting neck angles correct. String break angle makes virtually no different to tone or volume as long as you are keeping the strings in firm contact while picking, more than 15 degrees is too much for the cones, and less than 4 degrees the string start to bounce if you play hard. Once you get the neck shimmed OK, and you are stringing up and seeing what you have, you can fine tune the action height by adjusting the height of the bridge insert. Obviously action height and string angles are a far bigger deal with a round neck that is going to be played finger style and you need that good action, you can get away with a lot when you play lap style or even bottleneck slide, I play my 1935 Dobro round neck with a bottle neck slide because the neck has a ton of relief and the action height is around 3/16" at the 12th fret. With a square neck your string height off the fretboard is typically around 3/8".
You need to make sure the cones and the bridge is in the right place for intonation compensation based on if it's a round neck or a square neck. If it's a round neck to be played spanish style (fingers on the frets) you need compensation, so you want the front edge of the bridge insert to be aound 1/8" longer than scale length for the high string and about 3/16" longer than scale length for the low string, and you can adjust from there based on your string gauges and tuning. Scale length is twice the distance from the nut to the center of the 12th fret, usually Nationals were 25" scale, so you would initially locate your bridge insert 25 1/8" to 25 3/16" from the nut and fine tune after you string up. If it's a square neck you locate the bridge insert at exactly scale length for both strings, there is no compensation required with a square neck. I don't bother compensating a bottleneck slide guitar either, for the same reasons - no need to compensate for fretting action if you don't use the frets.
As far as cleaning the gunk, there is a fine line between dirt and patina, in my view. I probably wouldn't go much farther than vacumming out the inside of dust bunnies and wiping with naptha. If it's a steel body and it's gone rusty, that's a decision you need to make, same with the condition of any lacquer on the body or neck. They are neat old guitars and well worth engaging the services of either National or a qualified National luthier if you feel you are getting in over your head.
Edit: if you look at the link I posted you can see that the luthier purposely over-set the neck to get a high bridge height, a high break angle of around 15 degrees, and used a rosewood bridge insert. I wouldn't have gone so high, personally, but as he points out it leaves room for a few decades worth of lowering before it has to be done again. I also don't think heat-pressing a bowed neck is a perfect long term solution, but with a fretboard plane and new frets, it might last a long time.