Alright so to answer your questions

Mash

-don't worry about headspace, lots of guys are using a pretty much open container such as a brute trashcan for fermentation. It is much less finicky than wine or even beer since it only ferments for a week or two, then is distilled out.

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-I use electric now but the first couple of runs I did on propane were fine on one 20lb tank. I set it fairly hot for the heat up phase, but it gets turned WAY down when you're actually running

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-I make beer in a very similar mash tun. I have a copper manifold in the bottom but CPVC should be fine. Careful though PVC is only food safe to 140 which isn't high enough for mashing. Corn is supposed to be more gooey than most beer mashes so you may be running a risk of stuck mashes, I'm not sure how the enzymes will effect that.

Still

- That condenser is probably overkill, but I would always rather go more than less. For a shotgun you basically count the total tube length as a liebig using the calculator at homedistiller. That should give you a good idea of the knockdown.

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-you're not going to want to use plastic tubing for collection. Its not as bad as in the vapor path but still to be avoided. I personally use a length of copper tubing that comes back down to table height on my LM setup. Its pretty cheap and flexible. I also use a compression style fitting so it can be easily twisted and removed. If you have a link to the specific shotgun you are buying or diagrams of what you're building I could get more specific advice.

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- I use this pump in a 55 gallon barrel to cool. It's way overkill but I would rather have more flow than less. It has no problem pumping up about 8 ft to the top, and maintaining lots of flow through my condenser which looks like this. Its basically an inverted shotgun condenser so you would have no problems.

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I think you're on the right track, I would recommend setting up for pot still mode before you mess around with anything fancy though.