I bet they said that to barbara windsor in carry on camping .Once the wheel is off the nipple should shake out ok.
Rear spokes can be a bit of a swine as you probably need to get the cassette off to get it out unless its non drive side and you can maybe yank it out .Got the nipple out!
What about the spoke? Should I tape it up?
It will do, the rim is not tensioned where the missing spoke is so as soon as a new spoke is added and tensioned to balance the wheel it should be fine.(assuming whatever broke the spoke has not borked the rim )Although the back wheel looks a bit buckled when it is spinning. Can that be fixed?
First service I'd try for a new wheel out of em.Ok cool. Bike is due it's first service thing soon so will tape it for Wednesday/Thursday then drop it off at the weekend.