Inspection questions

Let's get the details out of the way. I am located in the Toronto, Ontario area using Langs for my hive. I have set up a new hive last weekend and verified that my queen was released by mid-week when I checked for that. The weather has been somewhat nice the past week but was raining off and on at times. I have been using a Pollen Pattie for food this week so far.

  I did my inspection this morning and things are looking good in other areas but some areas I am questioning. I can see they have started to draw comb out on the new frames I have given them. When I started to examine the existing frames from the Nuc, I noticed that they have been consuming the honey stores quite a bit. To remedy this, I have setup a syrup feeder with 1:1 mix. As I moved to the other frames, I am seeing the brood has hatched and is very empty. I am seeing larvae in spots, not huge clusters. As I looked through the frame I did see a few eggs; single egg per cell and place in the center towards the back. However, that is about all I saw for signs of the queen. I was watching for the queen, but I don't think I saw her yet. I saw a lot of drones.

Otherwise, the colony looks quite happy and busy as there is foraging happening, lots of bees around, and the frames are very populated. As well, the bees are quite calm and do not seem to mind me at all.
  The bottom line I am asking myself is: Do I still have a queen or not?

  Timing: Nuc was picked up on May 27, and installed that afternoon. I checked on the cage Wednesday evening and she was out. Today, I did my first inspection.

  Thank you in advance for reading and any help you can offer.