Is it permissible for the brother of a girl whose non-praying father has refused her marriage, in the absence of a Sharia court, to marry her off, or should the marriage contract be concluded and consummation postponed until the father is convinced?

The father is the most entitled to marry off his daughter, and his immorality does not negate his guardianship over her. It is not permissible for a more distant guardian to marry her off while a closer one is present, except in the case of obstruction (ʿaḍl). The father's refusal on the basis that his daughter will be far away is not a justification for refusal, while study and work are not impediments to marriage. Try to convince him, and if he does not agree, then look for someone else and entrust your affair to God, for He knows where the good lies.