Is it permissible for the wife to go out to study in a remote and dangerous place after sunset, without her husband's consent? And is it permissible for the husband to prevent her from doing so?

A woman should not leave her home unless the place and time are safe. Otherwise, she must be accompanied by a mahram (definition). Her departure must be for a need, while adhering to the etiquette of Islamic law: no tabarruj (displaying adornment), no perfuming herself, and no actions that might tempt men. What the husband did—forbidding his wife from going out at night on a dangerous path—is correct. However, the obedience of a wife who is only bound by the marriage contract (not yet consummated) is to her guardian, not to her husband.