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

A man is found dead in his bathroom naked with blood scattered all around him. The bathroom was locked from the inside and there is no trace of any struggle. There is nothing in the bathroom except his pant with the belt still around and his shirt. Also, the medic team can't find any incision in his body that may have been the reason behind so much blood loss.

The Police department is clueless regarding this murder mystery.
Can you?

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

Find the next number in the series.
1 10 24 43 67 ?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

Cristina was born in 1888. She just had her 30th birthday today how did that happen?

They do not possess flesh or feathers or scales or bone
But still, they are blessed with fingers and thumbs of their own.

No matter how little or how much you use me, you change me every month. What am I?

I was born in a small house and I live in it all alone. No windows and no doors have been assigned to my house. The only way I can go out is by breaking through the walls of my house.

Who am I?

I have nine bottles of wine and one of the nine bottles is poisoned.
I need to find the poisoned bottle with two facts
(1) Poison is deadly, only a sip will cost death
(2) I have two mice to do so.

How should I do it?