For clarification, the hive was originally installed almost a month ago, so if there was a virgin queen in there, shouldn't I have found brood by now?
If hive loses it's queen, it will take over 3 weeks and new queen start to lay eggs. If weather is good for mating.
I have taken two frames of brood from another colony and put them in now. Should I just wait, or should I try to order another queen after they've had the brood in there for a couple of days?
It is a little nuc. That is not able to raise good queen. Buy a new one.
Queen can also disapear during mating flight.
But you see after 2 days, if you have queen cells in brood frames, hive is queenless. If you have not, there is some kind of queen inside. It can be violated and not able to lay eggs,or worker size and difficult to notice.
I did install the previous queens by removing the cork from the candy end of the queen cage and poking a small hole through the candy, then I wedged the cage sreeen side down with the candy end slightly down between two center frames in the hive body. That's correct, isn't it?
It is correct often, if you are lucky. But often bees are angry and kill the queen with that method.
Only 100% way is make an isolated nuc over the hive, give emerging bees a frame, and not any adult bees. When nuc and hive has got same odour, it is safe to put together.
I do this because bought queens are valuable. With my own rased queens I do not bother myself so much.