was accidental or is it a brood and a half set up?
Might be both, but treat them as boxes rather than designated areas. If the colony is strong you may wish to give more brood space by adding another BB.
Take off the super, put into the middle of the new BB a few frames of open brood from the bottom BB, centre the brood frames in the bottom box, add frames of foundation to the flanks of both boxes and re-assemble. If you didn't see the queen, shake all the super bees into the BB, put on a QX and then the super. If that super is full, add another under it.
You may not want to use a QX (or have one). Don't worry, just add the boxes as above and by late summer the supers will be full of honey and empty of brood.
When I do a full inspection what should I look for?
Five basics:
Status: queenright? Tick brood in all stages (BIAS)
Status 2: queen cells? have plan & kit to act; if in doubt, nuc the queen
Disease: Check advanced open brood for unusual larvae
Space: room to lay & room to store; if in doubt, add more
Stores: 2 x DN4 frames of honey or equivalent is enough to last another week
Should I continue with the same set up, add a super for honey or is it too late now?
This tells me that you're not quite in sync with the three elements of beekeeping: basic life cycle & biology, equipment and how to use it, and the environment which determines the trajectory of the first two.
Set-up will be determined by the colony size: how many frames of brood are there, and are the current boxes rammed? As colonies are still expanding, another box may be appropriate.
The spring flow is slowing down south but still lively, and you must train yourself to observe which nectar & pollen plants are in flower in your area, and whether the weather is working in their favour.
Most current relevant factor is that the main nectar flow is yet to start - lime, blackberry, sweet chestnut, borage, ivy - and the bees produced so far will provide your workforce on the main flow.
Have you a copy of
this book?