What does this Rebus Picture mean?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

What is harder to catch the faster you run?

John is found dead in a bare field. Nobody killed John,
John did not commit suicide.

Inspector Jacob found a bag just a few meters away from John which could save his life. What was in the bag?

Replace the question mark with the correct number.

2 + 2= 4
3 + 3= 18
4 + 4= 48
5 + 5= ?

You walk into an old horror house. It has no power or plumbing. Once inside, you see three doors. Each door has a number on it. Behind each door is a way for you to die. Behind door number one, you die by getting eaten by a lion. Behind door number two, you die by getting murdered. Behind door number three, you die by an electric chair. You can’t turn back, so you have to go through a door. Which door do you go through?

What word begins and ends with an E, but has only one letter?

Remove two matchsticks to make the below equation correct.

What does this below rebus puzzle mean?

In Greek mythology, the Sphinx sat outside of Thebes and asked this riddle of all travellers who passed by. If the traveller failed to solve the riddle, then the Sphinx killed him/her. And if the traveller answered the riddle correctly, then the Sphinx would destroy herself. The riddle:

What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?

Oedipus solved the riddle, and the Sphinx destroyed herself.