I have branches, but no fruit, trunk or leaves. What am I?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

If you're 8 feet away from a door and with each move you advance half the distance to the door. How many moves will it take to reach the door?

What work can one never finish?

A man looks at a painting in a museum and says, “Brothers and sisters I have none, but that man’s father is my father’s son.” Who is in the painting?

I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?

What comes
Once in a Year
Twice in a Month
4 times in a Week
6 times in a Day

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?