What is the ruling on residing in America to study Oriental Studies, which includes learning the Hebrew language, and is the salary resulting from this study lawful?

The general rule is not to reside in non-Muslim countries unless there is a necessity or a recognized need. If the specialization you are studying is not available in Muslim countries, then there is no harm in residing there to acquire knowledge, while being careful of anything that might corrupt your religion and morals. You are advised to fear Allah, associate with good people, and maintain congregational prayers and Friday prayers. It would have been better for you to marry and bring your wife with you. Studying a foreign language is not invalid; rather, it may be necessary for Muslims, and it might even reach the level of a fard kifaya (communal obligation), as Zayd ibn Thabit learned Syriac by the command of the Prophet, peace and blessings be upon him. The ruling on the salary follows the ruling on the work; if the work is permissible, then the salary is permissible.