Is it permissible for a woman to marry herself in the absence of a guardian or ruler, and is the guardian's implicit consent sufficient without the explicit utterance of offer and acceptance?

The basic principle is that the woman's guardian (wali) should solemnize her marriage contract. If a guardian is not available, then the authority falls to the ruler (Sultan), or to Islamic centers in non-Islamic countries. If the woman delegates a trustworthy and upright person to solemnize her marriage contract, that is sufficient. A marriage contract solemnized in secular courts is invalid due to the absence of conditions for validity and because it is not permissible for a disbeliever to solemnize the contract. However, if the contract is concluded in an Islamic center, there is no harm in having it documented by secular courts to prevent disputes.