1) The frequency will depend on the transformer and the load connected to it. As the load on the transformer is increased, the frequency will decrease.
2) Just use a ferrite with a more than a high enough power rating (always best to over-rate) for the circuit you're powering. The turns ratio, can be lower than you'd normally expect for a mains transformer because it's a flyback. Try 200 turns for the driver (D), 3 for the feedback (F) and 5 for the secondary (5). I'd recommend winding the driver, then the feed back and finally the secondary. Put a good layer of insulation tape between the feedback and the secondary. Note the phasing on the schematic.
How do you reduce the noise? You could add an inductor to the secondary side, I've edited the above schematic, see L1. The mains side should also have the a suppressor fitted.
For safety reasons C3 must be Y-rated and shouldn't be more than 5nF and if you can be certain of the polarity of the mains it's probably better to connect it to neutral. C3 helps to minimise EMI by diverting high frequency noise from the secondary side to the primary side. Its value is too low to pass enough 50/60Hz maind current to be harmful.
I've never build this circuit, it's just an idea. Always be careful when experimenting with mains voltage circuits. All creepage distances between the mains and DC side of this circuit should be >10mm. Test the circuit by connecting it in series with a 100W light bulb.