Does saying to someone, "By God, if you die and he is with you, you will enter the Fire," invalidate the speaker's deeds, by analogy with the Hadith Qudsi: "Who is he who takes an oath by Me, that I have forgiven him, whereas I have indeed forgiven him and invalidated your deeds"?

It is not permissible to hang amulets (tama'im), whether they contain Quranic verses or anything else, due to the general prohibition by the Prophet, peace and blessings be upon him. This is to block the means (sadd al-dhari'ah) and due to what it might cause in terms of disrespecting the Holy Quran. You must advise your colleague and warn him against hanging something when he does not know what is inside it. As for the statement, "By Allah, if you die with it on you, you will enter Hellfire," if the intention behind it is to threaten him with the consequence of doing such an act, then there is no harm in it. However, if the intention is to definitively assert that this person is among the people of Hellfire, then it is a mistake, because such a declaration can only be made based on a textual proof.

Hanging an amulet can be minor shirk (definition) (associating partners with Allah) if one believes it is merely a cause, and major shirk if one believes it can harm or benefit by itself.