If I had a Bag of Holding (like #2), I'd leave it at the bottom of the ocean. When the world eventually ran out of water, I'd go retrieve and and start selling water to people/countries at an extremely high price.
For #1, stand by, I need to find a quote then edit it in here.
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Ok, for #1 I'd build a bathroom over it. Then I'd stash the other one somewhere safe.
Both that idea, and the thing about a perpetual motion machine, relate back to, of course, Pratchett:
'One opened up in one of the cellars once, all by itself,' said the Dean. 'Just a round black hole. Anything you put in it just disappeared. So old Archchancellor Weatherwax had a privy built over it.'
'Very sensible idea,' said Ridcully, still looking thoughtful.
'We thought so too, until we found the other one that had opened in the attic. Turned out to be the other side of the same hole. I'm sure I don't need to draw you a picture.'
'I've never heard of these!' said Ponder Stibbons. The possibilities are amazing!'
'Everyone says that when they first hear about them,' said the Senior Wrangler. 'But when you've been a wizard as long as I have, my boy, you'll learn that as soon as you find anything that offers amazing possibilities for the improvement of the human condition it's best to put the lid back on and pretend it never happened.'
'But if you could get one to open above another you could drop something through the bottom hole and it'd come out of the top hole and fall through the bottom hole again . . . It'd reach meteoritic speed and the amount of power you could generate would be---'
'That's pretty much what happened between the attic and the cellar,' said the Dean, taking a cold chicken leg. 'Thank goodness for air friction, that's all I'll say.'
Anyway, I'd put the bottom one over the top, separated by a coil of wires, sealed tight. Inside, I'd suck out the air (to get rid of air friction). Then I'd drop a magnet in the middle, so that when it came out the top it would fall through the coil and go back to the bottom. Bam, infinite power source until the magnet wears out.