What is the ruling on people saying, as they walk with the funeral procession, “Hudhu” (or “Say: There is no god but Allah”)? And is it prescribed to give a sermon after the burial?

The Shaykh : As for people saying, as they walk with the funeral procession, “Hudhu” or “Say: There is no god but Allah” or the like, there is no basis for this in the Sunnah either. Rather, one should accompany the funeral as I mentioned earlier, being humble, reflecting, and contemplating one’s own fate.
As for giving a sermon after the burial, this has no basis; it was not reported from the Prophet (peace and blessings be upon him). What was reported from the Messenger (peace and blessings be upon him) is that the sermon is delivered while sitting, not while standing and delivering a khutbah. It was reported as being delivered while sitting when they were waiting for what? The leveling of the grave. But if the grave is ready, the people will be occupied with the burial, and it is not appropriate to give a sermon in this case because it hinders the promptness of the burial. As for the sermon after the burial, it has no basis whatsoever. When the Messenger (peace and blessings be upon him) finished the burial, he did not preach to the people, even though he was the most eager of people to convey the message and the most wise in conveying it. Rather, he would stand and say, “Seek forgiveness for your brother and ask Allah to grant him steadfastness.” Yes.