Solution:

The killer is Alice.
The number in front of the month's name in the note actually points towards the position of a particular letter in every month.
Second of January = A
Third of July = L
Fourth of April = I
Second of October = C
Fourth of December = E.

Thus, the name is Alice.

Solution:

The murderer is Soumya because 26 Jan is a national holiday in India and the municipality office remains closed.

Solution:

It is not Richard because if it was, Richard 1 and Morgan 3 would both be false, which would make Richard 2 and Morgan 2 both true which is a contradiction.

It is not Travis because if it was, Travis 1 and Travis 3 would both be false, which is not possible.

Therefore, the killer must be Morgan.

Solution:

This is what Birbal said after bowing in front of the real king:
"Your majesty, the other kings were watching you closely in order to imitate you accurately while you were sitting with your calm and composed demeanor. This is how I found out that you are the real king."

His Quick wit flabbergasted the king and he was rewarded with luxurious gifts and jewels in return.

Solution:

AMAN

Explanation:
The numbers actually corresponds to the months of the year.

4 - April
5 - May
8 - August
11 - November

Now when you combine the initials of these months, you will get the killer's name i.e. AMAN

Solution:

The man had jumped from an aircraft and when he tried opening his parachute, he was unsuccessful. He hit the ground crushing all his bones and died on the spot. The unopened package found near his body is the parachute.

Solution:

Molly

Explanation:
Let us suppose that Patrick was not in the second bedroom. This proposes that Jerry, Molly, Max and Mike are liars. It infers that Patrick and Catherine speak truth. But that is not possible as they do not coincide on Mike's location. Therefore, we are wrong with our assumption and Patrick was in the second bedroom.
So far, we have established the fact that Patrick was in the second bedroom. Additionally, Patrick and Catherine are liars

Now, let us suppose that Jerry speaks truth. This proposes that Max was in the bathroom and Jerry in the second bedroom. This infers that Molly and Max are liars as they told that Jerry was not in the second bedroom. Also it implies that Mike lied, as he said Max was in kitchen. Therefore we have three new liars now, which totals the number of liars to 5, which contradicts the given situation in the question.
Hence, now we have established the fact that Jerry is a liar.

Let us now suppose that Molly speaks truth. This proposes that Jerry was in the living room and Max was in the Kitchen. This infers that Max and Mike are liars. But again, this is contradicting the situation as we have already established the fact that there are again 5 liars (counting above 3 established liars)
Therefore, now we have established that Molly is a liar. Max and Mike speak truth. Catherine was in the bathroom. Jerry was in the first bedroom. Max was in the kitchen. Mike was in second bedroom with Patrick.

The killer has to be Molly as no one else was present in the living room.

Solution:

The dead man used an ice knife to commit suicide. The ice held the knife pointing upwards as he dropped on the chair with his back facing the knife. Later, the ice melted leaving moisture around the body.

Solution:

It is quite possible. The poison was not on the drink but in the middle of ice cubes. The first one drank immediately and thus the poison could not reach his body while when the other drank after half an hour, the ice cubes had melted. Thus he died.

Solution:

The guy was killed a long ago, but he could not realize it till he reached his room. No need to be confused. Actually the killer has somehow inserted an extremely fine and thin incision blade in the belt of the guy. The guy did not feel anything at the moment as it was extremely fine. But when he was changing his clothes and took of his pant, the incision knife that was in his body, came out stuck to the belt cutting him very finely on the insides. That is the reason there was so much blood loss that he died and it was so fine that it was not visible to the naked eyes.