I asked Anas, "Was it a custom of the companions of the Prophet ﷺ to shake hands with one another?" He said, "Yes."  

قُلْتُ لأَنَسٍ أَكَانَتِ الْمُصَافَحَةُ فِي أَصْحَابِ النَّبِيِّ ﷺ قَالَ نَعَمْ  

When the people of the Yemen came, the Messenger of Allah ﷺ said: The people of the Yemen have come to you and they are first to shake hands.  

قَالَ رَسُولُ اللَّهِ ﷺ قَدْ جَاءَكُمْ أَهْلُ الْيَمَنِ وَهُمْ أَوَّلُ مَنْ جَاءَ بِالْمُصَافَحَةِ  

The Prophet ﷺ said: Two Muslims will not meet and shake hands having their sins forgiven them before they separate.  

قَالَ رَسُولُ اللَّهِ ﷺ مَا مِنْ مُسْلِمَيْنِ يَلْتَقِيَانِ فَيَتَصَافَحَانِ إِلاَّ غُفِرَ لَهُمَا قَبْلَ أَنْ يَفْتَرِقَا  

that a man said: "O Messenger of Allah! When a man among us meets his brother or his friend should he bow to him?" He said: "No." The man continued: "Should he embrace him and kiss him?" He said: "No." He said: "Should he take his hand and shake it?" He said: "Yes."  

رَجُلٌ يَا رَسُولَ اللَّهِ الرَّجُلُ مِنَّا يَلْقَى أَخَاهُ أَوْ صَدِيقَهُ أَيَنْحَنِي لَهُ قَالَ لاَ قَالَ أَفَيَلْتَزِمُهُ وَيُقَبِّلُهُ قَالَ لاَ قَالَ أَفَيَأْخُذُ بِيَدِهِ وَيُصَافِحُهُ قَالَ نَعَمْ  

Ibn Umar told a story and said: We then came near the Prophet ﷺ and kissed his hand.  

فَدَنَوْنَا يَعْنِي مِنَ النَّبِيِّ ﷺ فَقَبَّلْنَا يَدَهُ  

"Zaid bin Harithah arrived in Al-Madinah while the Messenger of Allah ﷺ was in his house. So he went and knocked at the door, so the Messenger of Allah ﷺ stood naked (1), dragging his garment - and by Allah! I did not see him naked before nor afterwards - and he hugged him and kissed him." (1) They say that the meaning of naked here is that he was not wearing his Rida or upper wrap and it was that which was dragging, so the area between the navel and knees were covered. See Tuhfat Al-Ahwadhi.  

قَدِمَ زَيْدُ بْنُ حَارِثَةَ الْمَدِينَةَ وَرَسُولُ اللَّهِ ﷺ فِي بَيْتِي فَأَتَاهُ فَقَرَعَ الْبَابَ فَقَامَ إِلَيْهِ رَسُولُ اللَّهِ ﷺ عُرْيَانًا يَجُرُّ ثَوْبَهُ وَاللَّهِ مَا رَأَيْتُهُ عُرْيَانًا قَبْلَهُ وَلاَ بَعْدَهُ فَاعْتَنَقَهُ وَقَبَّلَهُ  

Allah's Apostle ﷺ said to me: Don't consider anything insignificant out of good things even if it is that you meet your brother with a cheerful countenance.  

لِيَ النَّبِيُّ ﷺ لاَ تَحْقِرَنَّ مِنَ الْمَعْرُوفِ شَيْئًا وَلَوْ أَنْ تَلْقَى أَخَاكَ بِوَجْهٍ طَلْقٍ  

The Messenger of Allah ﷺ kissed al-Hasan b. ʿAli (his grandchild) while al-Aqra b. Habis al-Tamimi was sitting beside him. al-Aqra said, "I have ten children and I have never kissed anyone of them," Messenger of Allah ﷺ cast a look at him and said, "Whoever is not merciful to others will not be shown Mercy ˹by Allah˺."  

قَبَّلَ رَسُولُ اللَّهِ ﷺ الْحَسَنَ بْنَ عَلِيٍّ وَعِنْدَهُ الأَقْرَعُ بْنُ حَابِسٍ التَّمِيمِيُّ جَالِسًا. فَقَالَ الأَقْرَعُ: إِنَّ لِي عَشَرَةً مِنَ الْوَلَدِ مَا قَبَّلْتُ مِنْهُمْ أَحَدًا! فَنَظَرَ إِلَيْهِ رَسُولُ اللَّهِ ﷺ ثُمَّ قَالَ: «مَنْ لاَ يَرْحَمُ لاَ يُرْحَمُ.»