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

During prayer I made low mmm sound while thinking about something for a second. I completed my prayer because I have bad waswas that always makes me think my prayer is invalid. But is my prayer valid if I made this sound?

Prayer | May 20, 2015 5:28 pm
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“The person who is praying behind an imam should not move to the next posture of the prayer until the imam has reached it”. Some imams say the takbeer after they have reached the next position, some say it before they have reached. When should I start moving towards the next position? With the takbeer or after the takbeer?