My Haro V1 mountain bike’s chain falls off sometimes, and sometimes grinds and skips a bit… help!?

I want to fix these problems. When I shift down (3 to 2 or 2 to 1) the chain occasionally falls off the gears, requiring me to shift up (with the 1, 2, 3 options) again to get it back on. And sometimes when I pedal uphill, the gears/chain grinds and skips a bunch of spots… How can I fix these problems?

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