I’m from up here in Washington State. But bees are bees… From your pix’s it looks like your bees are off to a great start.
As for the entrance reducer. Here are some of my varied reducers. My actual Flow-hive is in its second season, very healthy n lots of inhabitance (defense). I don’t currently need a entrance reducer. But my four new Nuc’s I have varied styles but still don’t see evidence of Robbing … It’s a bit chilly – rainy Spring up here n we have a lot of bloom so guessing not much push for the “Robbing-Factor”. I’d check with several local beekeeper … So you have some real local knowledge of weather the region is in a nectar dearth or flower festive celebration with plenty to dine on !!
Now, how to refill that internal frame feeder. I don’t use them because they are too small n need refilled every few days n i don’t like interrupting the new colony that much. I’m not family with that style. Maybe Dawn or other U.S. Beekeepers have input n/or experience with the frame type feeder.
I personal use either purchased top-Feeder ( See photo)
And here is an example of double jar quart jar feeder that’s also easy to check n refill without disrupting your “girls”.
Good luck n happy beekeeping,