My landlord has filed for an eviction and we have a court date next week. Will we bee evicted at that time or how long do we have? What is the most you can be late with rent before they will file for eviction?

If you are late, and don't pay, they can ask for eviction, I would assume it was a pay or quit notice prior to filing in court.

Sometimes in court if you can pay all late payments, all late fees and court fees, they will let you stay.
If not, normally they will give you from 3 days to one week to move, but can give more, in some cases, elderly , children in winter, I have seen 30 days allowed