Take one out and scratch my head, I am now black but once was red. What am I?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

I am a ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

Can you count the number of triangles inside a triangle?

Two old friends, Jack and Jill, meet after a long time, and discussing as:

Jack: Hey, how are you, man?

Bill: Not bad, got married and I have three kids now.

Jack: That's awesome. How old are they?

Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.

Jack: Cool..But I still don't know.

Bill: My eldest kid just started taking piano lessons.

Jack: Oh, now I get it.

How old are Bill's kids?

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

Solve the equation by replacing the alphabet with numbers.

MOM + MOM + NO = BOOK=

How can you make the following equation true by drawing only one straight line: 5+5+5=550 ?

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

John was visiting his friend Jacob. He found out that his friend's wife had just killed a burglar in self-defense.
John asks Jacob about what happened and he told that "His wife was watching television when suddenly the bell rang. She thought that it is her husband Jacob but she found the burglar who attacked her instantly and she got so frightened that she killed the burglar immediately with the knife.
John asked the police to arrest his friend's wife. Why?