Does divorce occur in the mentioned cases, which are: the husband's saying "You are divorced" or "Divorced" while angry; his saying, "If you have done such-and-such, then consider yourself divorced"; and his saying, "If you go to a male doctor and he examines you, then you are divorced, except in cases of extreme necessity," and then she was compelled to go to a male doctor?

Issuing a fatwa (definition) remotely is not suitable for such matters. The correct approach is for the husband to directly consult trustworthy scholars specialized in issuing fatwas. As for the general ruling from a Sharia (definition) perspective:

Firstly: If the wife claims divorce and the husband denies it, his word is taken, unless the wife is certain that a triple divorce has occurred, in which case she must free herself from him through khul’ or similar means.

Secondly: A divorce that is immediately pronounced with clear wording takes effect without the need for an intention.

Thirdly: Most scholars hold that anger that does not completely remove one’s sanity does not prevent divorce from occurring. A divorce conditioned on an event occurs when the conditioned event happens, whether the intention was to effect a divorce or merely to threaten.

Fourthly: The occurrence of a conditional divorce depends on knowing what the husband intended by his oath.

Fifthly: If there is doubt about the divorce or about the occurrence of the condition upon which the husband made the divorce contingent, the divorce does not take effect because the default principle is the continuation of the marriage.