D. burmannii is easy, but sometimes it just doesn't take. There's really no getting it right or wrong - prep your pots with the right type of soil, put the seeds on top, and keep it wet with CP-safe water. That's it. My first try with D. burmannii yielded an enormous tray of plants, but my second try, a crop of seed that came from my first generation plants, returned far less adult plants than the first, even though I used vastly more seed and used essentially the same practices. Like Alex said, some so-called 'easy' species just don't work in all situations. I've had batches of P. lusitanica fail on me for no reason at all, and others go gangbusters. And I couldn't get my D. spatulata to produce viable seed if my life depended on it.
My advice is to put your sowed pots into a tray next to some common Drosera that does well in your collection, such as a D. capensis. So long as the common plant is OK, you're doing everything right. In my experience, D. burmannii has highly variable germination and maturation times, but you should probably see the first teeny tiny seedlings after three weeks or so. Times are different to maturity - I have some plants that are the size of dimes and producting flowers, and others larger than quarters that still seem to be in juvenile growth. At the very least, you probably have at least a month from germination to maturity, probably more, and chances are they won't flower until the days get short. When sowing, they go directly on top of the soil - the seeds and embryos inside are tiny and will be buried deep enough just by the soil that washes over them when you water. Fungicide might help, but is pretty much unnecessary unless you put the seeds in an unhealthy environment like one that's super humid or poorly lit. D. burmannii is called a weed for a reason - you don't have much to worry about. No, they don't commonly produce offsets, but they set seed in such quantities that it shouldn't be a problem. Even if you only get one plant out of your fifty-odd seeds, if it makes it to flowering, you shouldn't have any trouble keeping it in your collection.