Yes, generally you are right. However, if the pillar was performed during the prayer itself, the prayer is still valid as in the case of someone missing a sujood and remembering it before he concluded his prayer and hence he added another whole Rakah in exchange for the invalid Rakah.

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No, but you will be losing a great deal of reward and no house would be built for you in paradise.

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No, unless he authorizes you! Kindly refer to the following link(s): https://www.youtube.com/watch?v=PfAnP80AXUU

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