As of now (March 20, 2020), State Courts are effectively shut down, being open only for emergency business. Your definition of an emergency is not likely to be the same as the Court systems. If it’s not a matter of life or death, or some time of imminent harm that can’t be fixed by money, it’s probably not an emergency.
The operation of Federal Courts is much less centralized than that of State Courts, and I haven’t seen a blanket administrative order applicable to all Judges. That doesn’t mean one isn’t coming. In the meantime, things are on a Judge by Judge basis, but as a practical matter, everything appears to be getting adjourned in Federal Court. The Governor’s “stay in place” order shuts down most law firms anyway, so there isn’t going to be anything happening in Federal Courts, other than emergencies.
Evictions are on hold, even if the landlord has an order of eviction, he cannot execute it.
What does this mean for your case or intended case? Mostly it just means a delay. It’s like a time out. How long? Nobody really knows, but my take is that the government wants to stop new infections as much as possible, and then slowly ease up on the restrictions on public life. We’ll see first results in about two weeks. I would expect things to operate at about half capacity in a month, and barring any significant resurgence of the virus, we should be back to a semblance of normal in two to three months.
Of course, this could be wildly optimistic. I’ve heard doomsday scenarios from some people, but I don’t see a path to doomsday. Once people stop interacting with each other, the virus stops spreading, and once the virus stops spreading, all focus will be on returning to normal.
I’ll be working remotely and have access to almost everything in the files, as I’ve been fully digital for years. Feel free to call me or send me an email. I won’t be able to move cases forward much while the Courts are shut down, but I’m available to phone consultations and I can file new cases, as both the State and Federal Courts accept electronic filing of court papers.