[Machine] The Messenger of Allah ﷺ did not take off his shoes during prayer except once, and then people also took off their shoes. He asked, "Why did you do that?" They replied, "You took off your shoes, so we took off ours." He said, "Verily, Jibril (Gabriel), ﷺ , informed me that there is impurity in them (the shoes) due to the words of Ibrahim ibn al-Hajjaj, which Abdullah ibn al-Muthanna claimed as his own. Allah knows best. As for what Ibn Umar used to do regarding building during prayer, as well as sneezing and nosebleeds, we have narrated from Miswar ibn Makhramah that he used to say that it is recommended (mustahabb), which is based on analogy (qiyaas) to ablution in this matter. And with Allah is the success.  

أَنَّ رَسُولَ اللهِ ﷺ لَمْ يَخْلَعْ نَعْلَيْهِ فِي الصَّلَاةِ إِلَّا مَرَّةً فَخَلَعَ النَّاسُ فَقَالَ مَا لَكُمْ؟ قَالُوا خَلَعْتَ فَخَلَعْنَا فَقَالَ إِنَّ جَبْرَائِيلَ عَلَيْهِ السَّلَامُ أَخْبَرَنِي أَنَّ فِيهِمَا قَذَرًا لَفْظُ إِبْرَاهِيمَ بْنِ الْحَجَّاجِ تَفَرَّدَ بِهِ عَبْدُ اللهِ بْنُ الْمُثَنَّى وَاللهُ أَعْلَمُ وَأَمَّا الَّذِي كَانَ ابْنُ عُمَرَ يَفْعَلُهُ مِنَ الْبِنَاءِ عَلَى الصَّلَاةِ فِي هَذَا وَفِي الرُّعَافِ فَقَدْ رُوِّينَا عَنِ الْمِسْوَرِ بْنِ مَخْرَمَةَ أَنَّهُ كَانَ يَقُولُ يَسْتَأْنِفُ وَهُوَ الْقِيَاسُ عَلَى الْوُضُوءِ فِي هَذِهِ الْمَسْأَلَةِ وَبِاللهِ التَّوْفِيقُ