Which is the rope you never skip with?

Vin Diesel is pulling a theft and has planned to run away with all the cash kept in the safe. But the only way to open the safe is the 13 character password. He has a set of five clues given to him by a trustworthy source.

Exactly two of the below statements are false.
The password is contained within this sentence.
The password is not in this hint.
The password is within only one of these statements.
At least one of the above statements is a lie.

In four steps you need to move the word 'cold' From 'warm' by replacing one alphabet at a time such that every word formed at each step is acceptable in English Dictionary.

With the help clues provided in the image, can you find the 5 digit key?

How could a baby fall out of a twenty-story building onto the ground and live?

The below given figure comprises of a pattern through which you can determine the missing letter. Can you push your mind to find the pattern and add the missing letter?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

It's a test that will check your IQ.

Suppose you have one 11 minute hourglass and one 13 minute hourglass.

Can you measure exactly fifteen minutes using them ?