What is both possible and impossible at the same time?

Can you find any error in the following sentence?

A taxi was standing outside a fort at night. A man came out of the fort, opened the gate and hit the taxi driver killing him instantly. He took all the money out of the meter and started running till he was caught by a local sheriff.

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _

Can you find out the total number of triangles in the given figure?

A pet show was happening in my locality. I went down along with my kids. In that show, I noticed that all except two of the entries were cats. All except two were dogs and all except two were Monkeys.

Can you find out how many of each animals were present in that pet show?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?

The person who makes it has no need for it. He who purchases it does not use it. The person who does use it does not know they are. What is it?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

Nine marbles are arranged in the image below. Can you slide two marbles to form a square?