You have very different wines there. And obviously a lot of opinions. So here are mine.
Tawny Port- I’ve heard pretty much forever - Whatever you’ve heard, it’s not entirely correct. The deal with a tawny is that it’s already rather oxidized, so more air won’t damage it right away. It will last more than most of the other wines on your list. But it’s not a forever wine.
Vintage Port- I’ve heard must be drunk in one night - Just another wine. Some last a day or two or three. But I treat them like any red.
Sweet Riesling like BA and TBA - I find that wines with serious acidity hold up for a couple of days, but keep them in the fridge. And for me, they don’t last any longer than any other white. However, if you have a half bottle in the fridge, how can it possibly still be there after two days??
Vin Doux Naturel like Banyuls, Rivesaltes, Maury - These are like Port. They’re sweet because the fermentation was stopped by the addition of alcohol so there’s still unfermented sugar. But it all depends on how they’re kept. Typically they’re like a vintage Port - bottled and kept like that and I’d treat them as vintage Port. But you can find some that were left in barrels for many years. Those are more like a tawny Port and I’d treat those as tawny Port and they will last a lot longer. In fact, you can’t really find them, but some are more similar to Madeira than anything else.
Madeira- I’ve heard forever - This is the ONLY one for which that is probably correct. Everything bad that can happen to a wine has happened to these. They’re oxidized and heat-damaged and there’s nothing else you can do to them, so they will in fact last for a long long time. I’ve had them going back to the 1800s, and they’re still magnificent. But they’re not all sweet. Be sure to choose the sweet ones if that’s what you like.
Sherry (Oloroso and PX) - An oloroso is not sweet. It’s a very dry wine. And PX is a grape. If you make a sherry out of it, the PX sherry is usually sweet. But you can make dry wine from it. And you can make sherry out of Moscatel too, and those are much better IMO, because they’re not as sickeningly sweet as PX sherry, which for me, is hard to take. PX sherry is made from grapes that have been dried almost to raisins and it’s extremely thick and high in sugar. Both these and olorosos have been exposed to oxygen, so they won’t be damaged by being open for a while. Unlike Madeira, they haven’t been exposed to heat. Still, I’ve kept bottles open for nearly a year and they were fine. A sweetened oloroso, aka an “amoroso” has a bit of PX sherry added to it. Those are your cream sherries, etc., and that’s what you should look for if you want sweet, not an oloroso or Amontillado.
Tokaji - This simply means a wine that is from Tokaj. The “i” can be interpreted as “from” for simplicity’s sake. They can be dry, like Chablis, or late harvest, or really sweet, or not sweet at all if they’re made under flor like a sherry, or dry or sweet if they’re made like a ripasso. It’s too complicated to go into here but if you’re thinking of a sweet aszú wine, meaning it’s made from a base wine or must and dessicated berries, you don’t want to keep it too long. There are some that are oxidized, and under the communist jackboots the Russian overlords didn’t care as long as there was alcohol involved, so there was a lot of dark, oxidized, and usually crappy wine. But nobody today wants to make that. Well, maybe Hugh Johnson, since that’s what he got used to during the cold war, but even Royal Tokaj has finally moved away from that style, so beloved by the Brits. So treat these as you would any other white wine. The acidity can help hold it for a day or so, but you only want to keep it for weeks if you’d keep a Montrachet for weeks.
And a few you didn’t include:
Malaga - from the Málaga region of Spain. Made like a Port, so treat it like one.
Vin Santo - Hard to say. These are made by drying grapes on straw, which concentrates the sugars, but some are made in an oxidized style and some are not. The problem is it’s a style, not a region. Generally people think of it as a wine from white grapes like Trebbiano and non-oxidized. But it’s also made from red grapes and it can be oxidized. So depending on what you have, that’s what you want to treat it like. A non-oxidized wine won’t stay around too long, an oxidized one is more forgiving if you keep it around.
Sauternes - Treat it like a white wine. The extra sugar doesn’t really give it any extra life, and the lack of acidity as compared to something like Tokaji-aszú doesn’t give it any either. I don’t keep these for more than a day or two.
Ice wine - Treat it like a white wine. Again, the acidity is only there because of the removed water - remember that these are really really late harvest grapes.
Australian stickies - Never something I love as they’re typically too sweet. But they make some tawny styles, so those will hang around for a bit. They also do late harvest, etc., so go by the style.
Cane cut - these are kind of interesting. They’re like a combination of the straw wines and the late harvest, but once the canes are cut, there’s no more intercourse with the rest of the plant, so it’s only about what’s in the berries. They can be made in an oxidized style, but typically aren’t.
Brachetto d’Aqui - Not too sweet, young and bubbly, drink it the same day. One of the very best summer wines.
Moscato d’Asti - Also a good summer wine. Young and bubbly, drink it the same day.
Late Harvest Cab or anything else - Late harvest wines are usually best if not kept around too long.
Hope this helps. Some people may disagree. For me, the thing that keeps a wine alive is often acidity, which is why whites are usually better the next day than most reds. But another thing is simply size and if you have a wall of tannins and fruit, that can help too, and some reds are good for a few days. But in my experience, sugar is NOT something that acts as a preservative. It’s so powerful itself that a lot of people are happy just because they’re getting the sugar hit, but they’re missing much of the underlying wine if they keep things around too long.
But whatever blows your hair back. If you like to leave your wine around for a week or more, do so.