The STAR for most major airports is good to the holding fix. After that it's usually radar control. However, without radar the traffic would simply hold until the new runway was available and then commence approach.
The decision about which aircraft use the new runway is usually based on time. I.e. a decision is made to change runways at 14:35, so everything up to about 14:34 lands on the old runway and from 14:35 onwards they use the new one. It's very easy to do that under radar control but without radar there would usually be some delay.
Go-arounds against opposite direction arrivals... ATC would issue appropriate instructions to separate the aircraft.
How do they deal with departures?? The last one takes off at 14:34 from the old runway and the first one on the new runway goes a minute or so later. ATC provides separation between any conflicting traffic.
Runway changes depend on the weather. When a decision is made to change runways ATS usually has a long checklist of agencies to inform, eg the ATC Centre, safety services, etc. Runway changes at a major airport can take half an hour or more..