Hi Azhar,
By topology, we mean the intended class of SMPSU circuit you are going to use : There are lots !

Frequency. There are advantages to higher frequencies, there are disdvantages. Higher > smaller inductors. Higher > switching time problems. Its a trade off.

Transformer designs is much better understood to begin with, by reading books than just using web based "calculators", your problem was probably core saturation, from excess primary current, answer: more turns. But more turns = more resistance = more losses = more heat........

I haven't designed a mains powered switcher, my stuff has been dc-dc at low voltages apart from a pretty little He-Ne laser tube supply I built years ago. That was a Flyback converter topology.

Steve