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 guy threw a boomerang in the air from his window. It flew away and looped around to return back with high velocity. It hit his head and he died on the spot due to the injury. This can be the only logical explanation.

Solution:

The forest in which the body is found was on fire. Thus a fire fighting plane was appointed on the task of putting off the fire. The plane went to the nearest lake and scooped up the water to put on the fire. Accidentally while scooping up the water, they also picked up the man swimming in the lake. Unfortunately they did not know the fact and dropped him on the fir along with the water. He died on the spot.

Solution:

The blood came from a mosquito. It bit and sucked my blood last night. It then flew and sat on the ceiling. Determined to kill it I swatted it right there and the minuscule splatter came from it only.

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:

After five minutes, the second friend turned around to see if anyone was there or not. At this moment, he was stabbed on back by his friend.

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:

This is because Adam is a hangman by profession. Apparently, his wife has been sentenced to death and he had to do it with his own hands.

Solution:

Yes, the killer is Samoa. The numbers on the calendar represents the months and the initial of every month reflects the name of the killer.
9 – September (S)
4 – April (A)
5 – May (M)
10 – October (O)
8 – August (A)

Solution:

When he took the first bite of the salmon, he realized that what he ate at the island was not salmon but his friend