Yes in sha Allah your prayer is valid. You should not redo your prayer unless you have done something to invalidate it, otherwise you open the door to waswasa.http://islamqa.info/en/87749

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The best book is the description of the Prophet’s prayer by sheikh Al Albani.

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If you are traveling from one city to the other, you can shorten and combine before reaching your home. This is providing that the people of Dammam consider your home a traveling distance.

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