I’ll try to address as many of your questions as I can in roughly the order you asked them:
With respect to hydration, I’m using the term in the simplest sense – the percentage, by weight, of water compared to the flour. No probe or tool (other than a scale) is necessary to measure. For example 400g flour and 240g water would be 60% hydration dough. Keep in mind that different types/brands of flour can make quite different doughs at the same hydration %, so you will have to experiment with more or less water to find what works for you. I would suggest 60% as a starting point. For now, I would not worry much the humidity. I think it is among the least of your concerns.
As for oil in the dough, the biscuits, cookies, and other short breads you noted have way more than the 1-2% oil suggested for pizza dough. You are correct that in such “short breads” the oil, fat, etc (“shortening“) is shortening the gluten strands and making the dough tender. As the quantities suggested for pizza dough, it can make the dough more extensible by lubricating the protein strands and it should also help the dough to brown in the lower temperatures of a home oven. Some people also think it improves taste and texture and does other good things for the final product. I would encourage you to experiment with and without oil.
A good dough for you may windowpane, but that does not mean you would ever pull it that thin to make a pie, and I shudder to hear pizza dough compared to a condom… I think of windowpaning as a test (or a rite of passage maybe) and that’s it (and it’s kind of a useless test – either your dough performs as you want in your unique situation or it doesn’t, and if it does perform, who cares if it windowpanes, right?). I think you will find that when you achieve a smooth soft dough you will be able to windowpane it when it is well rested and relaxed, but once you prove to yourself you can stretch it that thin, you’ll never do it again.
My suggestion of the rest periods between relatively short kneading periods is just something that worked well for me when I had problems getting good flour years ago though I still do much the same thing today with good quality flour and am very happy with the results. I would hesitate to make the statement that resting is an important part of the process. I think a lot of people might disagree with such a statement. You don’t want to overwork the dough, but I doubt that is a big concern when kneading completely by hand.
A sealed plastic container would be great for raising the dough. You could also put the balls on a tray and put the whole tray inside a plastic garbage bag and fold the opening under the tray to keep it closed. Ether will keep a “skin” from forming on the balls when rising.
As far as the texture goes, I think you’re looking for a starting place where the dough can be easily worked without a lot of bench flour to keep it from sticking to your hands – certainly not “very wet, almost pudding like” as you noted. Even if it is a little tacky at first, resist the temptation to use flour to keep it from sticking to your hands. It will stop being tacky probably after the first or second rest and knead. On the other side of the spectrum, the dough should also not be so firm that it doesn’t flatten out at all when resting on the counter. I think JLP’s comment above on how the dough should feel is a good reference point.