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FAA Order JO 7110.65W - ATC Procedures, Chapter 10 outlines how ATC should handle procedures for emergency situations

Right at he very beginning, we see the most important part:

10-1-1(d) Because of the infinite variety of possible emergency situations, specific procedures cannot be prescribed. However, when you believe an emergency exists or is imminent, select and pursue a course of action which appears to be most appropriate under the circumstances and which most nearly conforms to the instructions in this manual.

In other words, they don't dictate what controllers should do in an emergency; they are to use their best judgment about how to handle it.

So, a controller is free to continue using a runway for both arrivals and departures if they believe doing so won't interfere with the emergency aircraft.

In fact, for non-urgent emergencies like gear extension failures, I've heard them hold the emergency aircraft to get as many others in and out as possible before the runway is closed for a gear-up landing.

Yes, generally speaking, the runway can be used. That said, whether or not it will actually be done depends on many different factors, such as the type of emergency, the size of the airport (maybe there are multiple runways), the current traffic load, the emergency response required etc. The fire marshall would most likely be the only person who could actually decide to close the runway, but ATC could, in practise, decide to not let anyone else land until the emergency is over. It depends.

From an ATC point of view, it may make more sense to get other flights on the ground before the emergency is due to land, instead of having to deal with airborne holdings and possible diversions. However, the risk of another aircraft breaking down and blocking the runway is non-zero, so if the inbound emergency has absolutely no other choice than to land on that specific runway, maybe just closing it for other traffic is the better option.

Most accidents don't give that amount of warning, but I was hoping for some information about United 232. Looking at the NTSB report AAR-90-06, pages 35-38, It gives the following items:

1. 1525 - The airport is notified of the incoming emergency. At this time it was not sure the plane would make it to the airport
2. 1547 - The fire chief is notified the plane is expected to make the airport, runway 31. Emergency response units line up along that runway (they later moved to runway 22)

Crash occurred at 1600.

Unfortunately the report does not indicate when the airport closed.