Howdy @FrankyHollywood! Excellent questions you wrote. I’m sure they’ll be useful for others, so let’s keep it up here. 
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Hmm, where specifically do you see that the shamisen isn’t insured? I can’t seem to find it, but if I missed it, it’s something I should correct as my partner does insure the shamisen.

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Ah, the part about not being responsible for broken skins is just for caution. Of the 400+ natural skinned shamisen we’ve sold, so far no skins have broken in shipping.

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Aah, sorry for the lack of clarification about the tenjin cover. (I believe it’s “Tenjinkake”?) It’s actually included with all our shamisen.

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Whoops! Thanks for letting me know that the link is broken! I’ll fix it. In the meantime, here’s the page it refers to - Caring for your Shamisen
Yeah, it’s totally fine to leave the shamisen on a stand inside, as you said, as long as the koma is off. 
Other than keeping dust off the instrument, there’s no real practical need for a fukuro if it’s kept inside.
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It should work, although I have to forcibly bend the two cushioned rods on the bottom of the stand closer together, as it’s sometimes a bit wide to rest under the dou.
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It really depends on how aggressive you’d be as a player, and your bachi technique. When played with the right fundamentals, one can get very crisp snappy tones with very little force (but that can take a while to get the feeling of), and thus make the same set of strings last for months. You’ll just have to play and see how it goes. And with that said, it never hurts to have extras.

Nothing you need to apologize for! I’m always grateful when folks spend time to research and ask questions so they start their shamisen journey with confidence!
Cheers!
Kyle