Solution:

Since every bacterium divides into two in two minutes and we know the fact that the dish was half filled with bacteria at 3 pm, after exactly 2 minutes, all will divide into two and will fill the petri dish. Thus, the petri dish will become full at 3:02 pm.

Solution:

Blue could only be wearing white or red and we know that there is already someone else wearing the white shirt so Mr. Blue could only be wearing the red shirt.

Mr. White could have only been wearing a blue or a red shirt, and red is already taken, so Mr. White is wearing a blue shirt.

Mr. Red now has to be wearing a white shirt.

Solution:

Sansa has the siamese (conjoined) twin sister.

Solution:

See the colored sticks in the picture. We have moved those sticks in the position given in the second image corresponding with the color.

Solution:

The Password.

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

Solution:

If the man killed himself, he would not have been able to rewind the cassette. Thus it is clear someone else killed him.

Solution:

They are matched as shown in the picture below.

Solution:

Old password : altered

New Password : distinct

Solution:

3 1 2 2 1 1
1 3 1 1 2 2 2 1

Read Line as one 1 => 1
Read Line 2 as two one => 2 1
Read Line 3 as one two and one one => 1 2 1 1
and so on.

Solution:

This statement is true but only in a specific case i.e. if both of the siblings continue to live till the day the younger is as old as the elder one was during the time of their birth.

Solution:

They were playing tennis.

Tiger Phil
30 - 30
40 - 30 (Phil hit a bad shot)
Game won - 30 (Tiger hit an awesome shot)