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Is my grandmother alive for some alien who is located on some place and is moving with some speed?
Events take place independently from each other, but speed of the effect to the cause is limited by the speed of light in vacuum. It's like "does a tree in the woods make a sound when it fells over when no one's listening?" - certainly. Reality doesn't need observers for things to happen.
Spaghettification of humans near black holes
Good point, I forgot to take into account that there are two feet. So actually I should be giving $2*m_F$ to the formula.