Is one who performs the obligatory prayer at the beginning of its prescribed time out of ostentation, without being aware of this ostentation, considered sinful, and is his prayer nullified?

We see that your question is a continuation of the intense سلسلة الوسوسة (obsessive whispering/doubts) you are suffering from regarding apostasy, disbelief, and hypocrisy. You mentioned that you are afflicted with obsessive doubts, so we advise you to fear Allah and stop giving in to these obsessive thoughts. As long as the person concerned does not know that he is a hypocrite, he is not a hypocrite.