Solution:

The Password.

Explanation:
Clues 2 and 5 are correct and rest are lies.

Solution:

Since the knife was in her hand which implies that she was planning to kill her husband "Inspector Montalbano".

Solution:

31

Explanation:
Ramanujan lighting the candles in binary.
11110 =30
11111 =31

Solution:

Selfie
Explanation:
: Selfie = is six letter word
: Self = The first four letter is me.
: e = The second and last letter are the same.
: fee = The fourth second and last letter are payment.

Solution:

Yes, you should switch the envelope. In the beginning when you picked up the envelope, you had a 1/3 probability of finding an offer letter in the envelope. There was 2/3 chance that the letter was there in the two envelopes on the table.

If you keep your selected envelope, you still have a 1/3 chance of finding an offer letter in that. However, since the interviewer has removed one empty envelope from the table, if you switch, you have a probability of 2/3 that the offer letter is inside that.

Solution:

Six.

There are only five colors, so six socks guarantee that two will be the same color.

Solution:

Playing chess

Game needs two players so Brother-8 is playing chess with Brother-2

Solution:

See the figure for the answer. Wasn't it a bit tricky?

Solution:

7

Explanation:
8th is bald man head, check the video below.

Solution:

It is best if the person sits on the back of the train. After the stop, the train will be accelerating as it goes into the tunnel. Thus the train will be much master when the back of the train enters the tunnel. In this way, he will have to spend much less time in the tunnel.

Solution:

1 2 3 4 5 6 and 7 8 6

Since summation of numbers 1-9(1 2 3 4 5 6 7 8 9) is 45 , so its impossible to divide into two equal parts.
Since we cant flip over 6 to make it 9 but we can flip 9 to make it 6 and hence the solution