Am I obligated to offer expiation after my nominal marriage to a man I only saw at the marriage ceremony, and am I obligated to observe the waiting period of divorced women, and when is it permissible for me to marry another man?

Firstly, it is not permissible to compel an adult woman to marry someone she does not desire. A contract made without her consent is either void or dependent on her approval.

Secondly, contracts in the courts of disbelieving countries may be valid if preceded by legitimate Islamic contracts that fulfill all conditions (offer, acceptance, guardian's consent, witnesses). Otherwise, they are void and no rulings can be based upon them.

Thirdly, marriage is a solemn covenant, and it is not permissible to enter into fictitious marriage contracts for the purpose of residency or citizenship. This is a mockery and trivialization of the Islamic contract. Fictitious contracts that fulfill all Islamic conditions will have their effects. However, if they are not conducted according to Islamic law, they will not have Islamic effects, though sin will be incurred.

In summary: If the marriage was concluded with the consent of the father, witnesses, and the wife's satisfaction, it is a legitimate contract and its effects apply. This marriage cannot be dissolved except through divorce and the waiting period ('iddah). However, if the contract was made only in official departments without the consent of the wife or her father, it is not legitimate and has no effects. A legitimate divorce is not necessary except to settle official documents, though the person responsible for it incurs sin. It is obligatory to be cautious and not finalize the new engagement until after divorcing the first. Informing the new suitor about what happened depends on the wife's estimation of how much he knows, while relying on Allah.