Solution:

SITA

19 = S
9 = I
20 = T
1 = A

Solution:

At 01:05

Solution:

The guard and the prisoner cross the river
The guard comes back
The guard and the girl cross the river.
The guard and the prisoner comes back.
The mother and the girl cross the river.
Mother comes back
The mother and the father cross the river
Father comes back
The guard and the prisoner cross the river
Mother comes back
The father and the mother cross the river
Father comes back
The father and the boy cross the river
The guard and the prisoner comes back
The guard and the boy cross the river
The guard comes back
The guard and the prisoner cross the river.

Solution:

She is near the trunk of the tree as shown below.

Solution:

2 minutes (duration between 9:59 and 10:01)

Solution:

The clerk said that every day the password is CHANGED. Changed is the password.

Solution:

Treasure Map Is Hidden Inside The Hanging Room Floor.

Explanation.
Just reverse the text "roolF mooR gnignaH ehT edisnI neddiH sI paM erusaerT".

Solution:

-3 -1 1

Explanation:
-3 * 1 * -1 = 3(prime)
-1 - (-3) = 1 -(-1) = 2

Solution:

The equation can be solved by substituting
B = 7
A = 8
S = 8
E = 3
L = 5

Therefore the equation now looks as:
7483 +
7455
-------
14938
-------

Solution:

5 leopard and one sheep

since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.

Solution:

Hockey Stick $49.50 & ball $0.50