My time was up so off I went, but they came and searched for me. They went door to door to try and find the person who owned what I left behind. Who am I?

Answer: Cinderella

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Some try to hide, some try to cheat, but time will show, we always will meet. Try as you might, to guess my name, I promise you'll know, when you I do claim. Who am I?
Sometimes you are so relieved to see me, and other times you run from me in fear. Sometimes I stop you and sometimes I let you go, but whenever you need me I am always a quick call away. Who am I?
T is on Me, T is in me ,my name starts with t .
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What can pass through water without getting wet? Who am I?
What starts with T, ends with T and is full of tea?
You are my sister but I am not your sister but somehow we are siblings. Who am I?
You can see me up north bundled up, I live inside a white house, and my diet is mainly Paleo. Who am I?
You move your arm, I do it back. You move your leg, I do it back. You close your eyes, but I can't do it. Who am I?
All men take off their hats to me. Who am I?
I am a born warrior, a princess and I have a rope that can destroy lies. Who am I?