What is full of holes but still holds water?

I am a normal creature, but I have five hands. I can even have more but even then I will be considered normal.

Who am I?

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

Can you find out the remainder when 3^300 is divided by 5?

I am something people love or hate. I change peoples appearances and thoughts. If a person takes care of them self I will go up even higher. To some people I will fool them. To others I am a mystery. Some people might want to try and hide me but I will show. No matter how hard people try I will Never go down. What am I?

How can you take 2 from 5 and leave 4?

Peter wakes up daily to pick up his cycle and crosses the border between Spain and France daily with a bag on his shoulder. He is investigated daily by the officials but they don't find anything suspicious.

If we tell you that he is smuggling something what would it be?

The Judge knows that Alamgir was killed by his girlfriend Jasline, but the judge is unsure whether to punish her. Why?

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?

In the image below, can you find the value of an angle(y)