Why the voltage across MOSFET (VDS) is increasing even when the voltage at the gate (VGS) is constant?
You're switching frequency is 40kHz and the inductances are 1uH. If you'd be probing the currents in the switches you'd have a revelation. Change them to be 100uH, for example, and watch the magic. How did you calculate them, btw?

Also, try to be a bit more tidy when drawing the schematic, at the very least for presentation purposes -- it's a pain to figure out all the connections as they are drawn now, and this is a small schematic.



Getting into transformer design would mean discussing an entire chapter of the behemoth that is electronics. Instead, here is a document which survived time (thank goodness): Designing Magnetic Components for High Frequency DC-DC Converters (a search should reveal this within the first results). As I said, there are other application notes on the subject, freely available on the Internet, which you are welcome to search for, yourself.