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

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

A man escapes from jail using help from his girlfriend. The investigators suspect four girls of being the man's girlfriend.

Out of those four girls, one is his girlfriend who is lying. Two of the girls are completely innocent and are speaking the truth. One of the girls is the man's sister who is helping the girlfriend lie. Following are the statements from all four of them:

Ariana: "Myrna is his girlfriend."
Jane: "Angelina is lying."
Angelina: "Ariana is lying."
Myrna: "Jane is not his sister."

Can you find out who is the man's sister among them?

Find the missing number in the sequence below:

What has to be broken before you can use it?

Rebus Puzzle Definition: A rebus is an illusion device that uses pictures to represent words or parts of words.
What does This Rebus Puzzle Identify?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

I am a type of room you cannot enter or leave. Raised from the ground below, I could be poisonous or a delicious treat. What am I?

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

What does it mean?