Is it permissible for a woman to travel without a mahram, and is she allowed to marry whomever she desires without her guardian's consent after he has refused to complete the marriage?

You are not permitted to marry this woman without the permission of her guardian, because marriage without a guardian is invalid. If the father prevents his daughter from marrying (idhal), then guardianship transfers from him to the ruler, not to the more distant guardian, unless his refusal is repeated three times. In that case, he becomes a transgressor (fasiq), and guardianship then transfers to the more distant guardian. It is not permissible to appoint a non-relative as an agent when a guardian exists. If there is no guardian or Muslim ruler, then the Muslim community can undertake the marriage contract, such as the Imam of the mosque marrying her.