What is the ruling on dealing with a Jewish Israeli female lawyer and agreeing to meet with an Israeli interrogation officer without a mahram in order to obtain a transit permit necessary for training and taking exams?

It is permissible for a Muslim to deal with and appoint a non-Muslim lawyer, because it falls under the category of permissible agency between a Muslim and a dhimmī. Therefore, there is no objection to hiring a Jewish female lawyer.

As for being alone with a foreign man, it is forbidden by Islamic law, and its prohibition increases if he is a non-Muslim foreigner. Thus, it is not permissible for you to meet with the aforementioned officer in a private setting, unless you are compelled to take this job and cannot find an alternative. In that case, you must adhere to modesty and dignity, avoid being submissive in speech, and limit the meeting to the extent of the necessity.