Are there English classes in the Hawza in Najaf? If not, what level of Arabic language understanding is needed to study there? And where can I find information on their courses?
Bismihi ta'ala
As far as there being an English speaking curriculum, or madarasa is concerned, in Najaf al-Ashraf, I do not think there is such an establishment.
However, I also do not recommend that if you were interested in joining the Hawzah, that you study only in English. It is imperative that a Hawzah student not only learns Arabic, but also masters it. Ultimately, you are going to be working not just with Arabic Hawzah texts, but also the Quran and hadith, and with deeper insight and stronger comprehension.
You will be able to pick up on the language quickly, and learn it like how all other non-Arabs have learnt it.
As for information, I have a FB page where I have put together some sources and material for Hawzah studies. Hopefully it will be of benefit:
https://www.facebook.com/Hawzah-Studies-Resource-Page-1424569624476422/
With prayers for your success.