Does the mere doubt of a scrupulous person regarding a vow make it binding, and is his saying to a Mufti, "I have made a vow," considered a confirmation of it? And is missing a prayer on time due to the unavailability of a prayer room at work, or saying, "I must stop working," considered a breach of a vow or another vow?

You are not permitted to delay the prayer beyond its prescribed time, even if you are outside the home. Your vow does not establish a ruling, whether it is the vow you are uncertain about, or what you told the Mufti, or what you uttered in colloquial speech. These whisperings (waswas) have reached a great extent within you, and we advise you to constantly supplicate and humble yourself before Allah, to distract yourself from these whisperings, and to consult a trustworthy psychiatrist. We also recommend that you have a good opinion of Allah and be optimistic that the new work circumstances will be more conducive to obedience to Allah. There is no objection to carrying a small prayer rug with you to pray on.