How valid is the warning against using the words "Dūm" (may it last/endure) and "Labbā" (here I am/at your service) and what follows them, on the basis that the Everlasting is Allah, and the "Talbiyah" (response to God's call) is for Allah, and does their use constitute shirk (polytheism)?

Responding to other than Allah with "Labbayk" is not polytheism (shirk (definition)). The Companions used to respond to the Prophet, peace and blessings be upon him, with "Labbayk." Among these instances is the saying of Mu'adh and Abu Dharr to him: "Labbayk, O Messenger of Allah, and Sa'dayk." Al-Bukhari and Abu Dawud dedicated chapters to the permissibility of this. It is also narrated that 'Umar ibn al-Khattab and 'Amr ibn al-'As exchanged this word, as did Abu Bakr and Bilal. Al-Nawawi explicitly stated its commendability.