the window gasket should not have a "diameter" (about 7/8ths" wide and flat!)... it has a "channel" so to speak in the middle of the flat that the edges of the glass rest in.
welding brass to steel is not happening unless you weld for a living (tig weld) and even then it would never be as strong as like materials (the filler would be some obscure bronze rod in attempt to make the mate between steel and brass).... no...just no.
The main weld on the corroded tab is on the underside (this is where i would have buried the weld deep and hot across the small length of that tab) doing this on the top side was not possible without getting "door ride up on the weld itself" (they were mig welded).... so though i agree that tab looks bad check the underside of it for strength (maybe just cleaning it up or worst case adding some weld).
the 1/2 inch door gasket only needs to be stretched enough to push it into the gasket slot on the stove. your ahead of the curve already because 90% of the folks who have cranes are unaware to use this forum... they use 3/8th gasket because thats what the slot measures and that is WRONG, it will not last or be as dense as the more proper 1/2" that is supposed to be used. (dont worry about the white gasket... it only means it wont last as long, it will work fine.
which end do crimped flu pipe go towards
... a common question here and very searchable using the search feature upper right corner of page. with a coal stove we like to see the crimps face the chimney (not the stove), with wood stoves its the opposite (for reasons you can review, it would take to long to explain here)... between you and me it really does not matter with regards to you since your a coal burner (either will work).... but again....if you have a choice, chose crimps facing chimney all the way out
its great to hear that your biggest hurdle here (the door hinges) are right up your alley and im sure you will be OK. If you do indeed have a welding machine and think you want to replace the tabs on the stove than simply get some steel barstock approx 1/2" x 1/4" and make some new tabs with that, you will grind down the existing tabs nice leaving only the contour of the stove edge, you will lay the stove on its back and take the doors (with NO gasket installed on them!), lay the doors on the stove center them to the openings, place a NO MORE than 1/8th" spacer on the hinge side and then place your new hinge tabs with pins into the door and make sure you can turn them all the way up (door open), and all the way down touching stove (door closed) .... now weld them bitches in place as she sits (remember, you cant weld the top portion well, so make damb sure your getting that underside GOOD!)
ok... your off and running! good luck with draft (im not sure how your going to judge draft to accurately without heat
)... ill let some other weight in on that stuff who are more knowledgeable with mano installs and draft readings.
P.S. while you have the doors off and apart take a nice (non-aggressive grinder), flexable 80 grit Norton or whatever and lightly grind nice and smooth the inside face of the door (along the gasket slots) to remove ANY possible casting "boogers" or rough bumps. this should take a brief minute and makes for super quality that sometimes gets lost in mass production