Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
There are some weak Ahadith that state wiping one's face after making Du'a. But Ibn Hajar (a great scholar of Hadith) consider these Ahadith together an evidence that such an act is good. Among these Ahadith what Al Tirmizi reported in his 'Sunan' that 'the Prophet (Sallallahu Alaihi wa Sallam) used to wipe his face with hands after making Du'a before putting them (his hands) down.'
Aslo, Abu Dawood and Ibn Majah reported from Ibn Abbas that the Prophet (Sallallahu Alaihi wa Sallam) said: "And when you finish (your Du'a) wipe your face with them (your hands)."
However, we did not find any text reported from the Prophet (Sallallahu Alaihi wa Sallam) about wiping one's face after the Imam's Du'a in Friday sermon (Kahutba).
It should be mentioned here that wiping the face is an act that follows raising the hands in Du'a and the Sunnah is that the Imam does not raise his hands in Du'a during Khutba.
Muslim reported that 'Umarah saw Bishr Ibn Marwan on the pulpit raising his hands and said: Allah, disfigure these hands! I have seen Allah's Messenger (peace be upon him) gesture no more than this with his hands, and he pointed with his forefinger.'
So, it is more appropriate for the Imam delivering the Khutba not to wipe his face after Du'a.
As for using beads (Tasbeeh) it is lawful and for more details about that please read Fatwa: 84295.
Allah knows best.