1. Greeting is one of the desirable acts that have been recommended.[1] It is not makrooh (abominable) to greet someone from this perspective. However, according to some religious authorities (maraje’), if not doing an action such as shaking hands is considered in common view as a way of mourning and expressing grief, it is better not to do it.[2]
2. Imam Baqir (as) was asked about how we should console each other on the Day of Ashura? The Imam answered: Say: "أعظَمَ اللهُ اجورَنابمُصابِنابِالحُسَینِ،وَجَعَلَناوایّاکُم مِنَ الطّالِبینَ بِثارِهِ مَع وَلیّهِ الامامِ المَهدیِّ مِن آلِ مُحَمَّدٍ(ع)" May God increase our rewards as a result of what has befallen us through Hussein’s sufferings. May God make both you and us men who seek vengeance for him together with his great successor (wali), the Imam, the Mahdi from the family of Muhammad (a).[3]
[1] Vide: The Importance of Greeting, 6923 (site: 7027).
[2] Tabrizi, Jawad, New Isteftaat, vol.1, p. 454, Qom, first edition (date and place of publication not known)
[3] Tusi, Muhammad bin al-Hasan, Mesbah al-Mujtahid wa Selah al-Muta’abbed, p. 772, Fiqh al-Shi’ah, Beirut, first edition, 1411 A.H.