What does this rebus riddle mean?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

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?

Take number 1000 and then add 20 to it.
Now add 1000 one more time.
Now add 30.
Now add 1000 one more time.
Now add 40.
Now add 1000 one more time.
Now add 10.

What is the total?

There is something which is always coming but never arrives?

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

A man has eighty-one cows ( numbered 1,2,3...81 as such). The beauty is that cow no. 1 gives 1ltr of milk, cow no. 2 gives 2ltrs of milk and so on. The man wants to equally distribute the cows among his nine sons so that each one of them gets the same quantity of milk.

A man is found dead with a knife in his back When the investigation is done. A chair lays beside him and the forensic team finds moisture around the body.

If he committed suicide, how did he do it?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?