What is the ruling on repairing mobile phones using the aforementioned mechanism, which involves taking half the amount in advance after determining the cost of the spare part and labor, then purchasing the part, repairing the device, and collecting the remaining amount?

There appears to be no objection to the questioner's work, which involves a lease for repair and an agency for purchasing spare parts. The lessee has the right to receive his full or partial payment in advance. It is permissible for the agent to take the price of what he is commissioned to buy in advance, as Urwah al-Bariqi did with the Prophet, peace and blessings be upon him. Since the questioner is an agent for purchasing spare parts and not a merchant in them, this action of his does not fall under selling what one does not possess.