My first question is always: "What are you trying to accomplish?"
When you're changing out so many parts you're usually economically better off to get a brand new bike because every single part will be brand new and designed to work with every other part. You'll also get a new bike warranty. The downside is that it isn't as much fun as doing it yourself. If you are delighted with the fit of the Gitane, it might be worth doing.
1. Spreading the stays will be easier than you think. You shouldn't have to do anything to the fork because front wheels have been 100mm OLD forever.
2. 1.37 x 24 means you have an English threaded bottom bracket. That's a good thing because they are easy to find. Since you're sticking with square taper you'll want to buy the crank puller that fits your Tioga crank. It'll fit your new Sugino crank too. Buy a splined bottom bracket tool to fit a new Shimano UN-52 or UN-72 cartridge bottom bracket. Do whatever you have to do to get your old one out.
3. Front derailleur is pretty much a toss up. An Ultegra or 105 is going to rub the top of the chainring while an LX is going to rub on the back. I think that I'd go with the road triple.
6. Bar end shifters are economical and you won't have to buy new brake levers. You'll have few, if any, front shifting issues with the friction shifting bar ends.
7. With a 30 tooth big cog an Ultegra or 105 derailleur is a stretch but can usually be made to work. An LX will work for sure. If I was buying a new one, that's what I'd get.
Good luck!