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1. Are plastic sleeves OK. The kind you get from the store for pictures or presentations? I got a whole box of them and was going to melt them (with my food saver )into little boxes with slits cut to put the stamp in, keeping the sheet whole so I could put it in a binder.
Not a good idea. Probably OK for most stamps short term, but not recommended for >1 year. And never store the stamps laying flat in those non-archival plastic sleeves. Some stamp/cancel inks will react with the plastic, accelerated by the pressure of other stamps/sheets on top of it. Always store your albums upright.
Proper stamp storage is something you should not try to cut down to bare minimum. Eventually, you will pay the price, and often it's with one of the more valuable stamps in your collection. A simple stamp stockbook is not as expensive as you might think.
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2. Whats the best way to separate stamps? I have a lot stuck together and tons still affixed to the covers that have been cut off.
If the stamps are not self-adhesive stamps, then soak them face down in cold water until you see the first few stamps start loosen from the paper (they will start sinking to the bottom). Avoid soaking the stamps for more than 30 minutes.
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3. Should I even remove them from the cut off covers or just cut it down?
4. If I have different stamps attached to cut off covers should I separate them or leave them together?
There will be differences of opinion here. See what the others have to say.
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5. I cleaned a stamp with diluted hydrogen peroxide, is that the only household chemical to use?
I don't recommend chemically cleaning/altering stamps. However, others will have a different opinion. Never used water-based solutions (such as hydrogen peroxide) on mint stamps -- you will lose the gum. Also, if you deliberately chemical clean/alter your stamps, it doesn't require an expert to recognize it. You should document it to avoid future issues regarding fraud.
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6. Drying stamps; ok on plain white paper?
Face down on blotting paper is better. I use face down on higher quality disposal paper towels (e.g., Viva, which has much less fiber release) or very high thread count clean room quality cotton wipes (reusable). To keep the stamps flat while they completely dry, I press them with an Imperial Drying Book (combination of blotting pages and glossy-faced pages -- almost nothing will stick to the glossy-faced pages).
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7. Is there a definitive way to tell if a stamp has never been hinged except for checking for a cancel, and all the gum on the back looks like it's still there?
That is the standard way and good enough for >99% of stamps. When you get into regumming problems, then it gets more complicated.
Enjoy your stamps!

k