The pic of the wire shows a joint which hasn't wet correctly. You can avoid this by covering both wires in solder before attempting to join them. That way it is also easier to avoid melting the cable insulation.
But I tried at around 225°C (between 200°C - 250°C), the solder still melt well.
Yes it melts somewhere around that temperature. Generally, the temperature used depends on your skill. It's often easier for beginners to set the iron at 250°C, then you can hold the tip against the joint longer. Professionals who solder quick usually use around 350°C. Higher temperature also means shorter tip life.
But please note that this depends a lot on what solder iron you use. The quality brands measure temperature at the tip, cheaper ones just sets some fixed temperature.
the lead free solder surface should be dull as everyone is saying. For my trial, it gets shinny surface and of course dull surface also
It should get grainy. Compared to a leaded solder joint it will look dull, but when using RoHS solder you can usually tell the difference between a good joint and a cold joint still. Some of the joints in the pic look fine, others where part of the via is still visible have not wet properly. I would suspect a temperature issue to be the cause, it looks like only part of the via got sufficiently heated. As others have mentioned, you should try a broader tip when that happens. Using external flux is always nice too - sometimes if you heat the joint too long all flux in the cord will vaporize.
Also if you want to do it by the book, cut through-hole components like in your picture to the correct length before you solder. They should be cut to somewhere around 0.5mm to 1.5mm at most, not longer.