Solve below rebus puzzle?

Can you decipher the two rows to find the hidden word?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

You are stuck on an island where you have nothing. You find four pieces of paper somewhere on the island. What will be your strategy to escape from the island safely?

PS: No other resource is available to you on the island, neither can you build anything.

Replace each alphabet with the number (1-9) to make the below equation correct.

AB * C = DE - F = GH / I

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

Let's play a word game. Following are some meaningless words that can be completed by adding random letters on either side of the word.

For example, the word "rdo" can be formed into "pardon".

Using the same technique, can you complete the given words?
ecalc
airb
rinci
tibac
uidel
gorit
igna
eyho

2, 3, 5, 9, 17, _ What is the next number in the sequence?