Is it permissible to break one's fast with unlawfully acquired money, and is it obligatory to re-fast the day on which this occurred?

You must sincerely repent from the sin and return the money taken unlawfully to its rightful owners. Otherwise, the reward of your fasting may be nullified and its recompense lost, as the Prophet, peace and blessings be upon him, said: "Whoever does not give up false speech and acting upon it, and ignorance, Allah has no need of his giving up his food and drink." Your breaking your fast with this money is forbidden, and while the fast itself is valid, its reward may be withheld if you do not repent.