WOW! I'm doing almost exactly the same thing!
I have an old Hondo LP copy that is a flat top and I've run it through a thicknesser and I'll putting a drop on it.
My top will be a book matched pair and I'll be doing a dark sunburst finish. I'll also be putting a new set of pickups in it.
As for your questions, as a newbie myself I wont answer any just cos I don't feel qualified yet
I will say this though, expect to get some resistance to this project from a few blokes cos it's not exactly the easiest or the most sensible way to to do it.
AND don't expect it to be as straight forward as a dropping a top on, painiting it and playing it.
You well need to consider important things like neck angle since the thickness of the guitar will effect the height at which your bridge is gonna sit in relation to the depth of the neck pocket. If this is something you haven't considered or you're not across all the details of neck angle there is some great info pinned on this forum to help you work it out.
I'd also say if you're just going for a new look that's cool, but if you're hoping its gonna sound better, it probably wont unless you wack some pickups in it that are specific to the era you're going for.
The last thing I'd say is that I thought the carve top on all the LP's of that era were made of maple (mahogany body/maple top)(I MIGHT BE WRONG!). You mentioned you had the Mahogany to laminate to your body. Without a maple top your LP probably wont sound much like a '50's LP. Just something to consider. (I should note that my one is gonna have Australian Blackwood top NOT a maple top...but then I'm not trying to emulate the '50 sound, I'm going for something a little different).
Good luck with it...I'll be watching with interest. I'll be posting a thread for my own rebuild pretty soon maybe we can learn a thing or two from each other.