What goes up but never comes down?

A man calls his dog from the opposite side of a river. The dog crosses the river without a bridge or a boat and manages to not get wet. How is this possible?

Can you identify the hidden rebus in the image below?

What can you hold in your right hand, but never in your left hand?

You are in a room that has three switches and a closed door. The switches control three light bulbs on the other side of the door. Once you open the door, you may never touch the switches again. How can you definitively tell which switch is connected to each of the light bulbs?

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

Can you decipher these quotes by Albert Einstein?
Blf xzm mvevi hloev z kilyovn lm gsv ovevo lm dsrxs rg dzh xivzgvw.

Rearrange the letters in "new door" to make one word.

Can you divide numbers from 1 to 9 (1 2 3 4 5 6 7 8 9) into two groups so that the sum of the numbers of each group is equal?

Note: 9 cannot be turned over to make it 6.

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?