If B4 button 0,1sn pressed...
Then X4 0,1sn operated and DS 0,1sn active.
(DS --> 1-3sn active to be). So you want to limit the time that DS is energised regardless of how long B4 is pressed. If so, then you will need to do more than just making X4 slow to release....
So ;
If B4 button 10sn or more pressed...
Then X4 10sn or more operated and DS 10sn or more active...
This is a problem for DS...(DS is break down !). Yes, DS is likely to over heat and burn....
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Series resistor (82 Ohm) is only for charge required. Yes, but it makes little difference to the release time. As I said previously, this is a standard technique used to increase relay release time.
I have never seen a diode across the resistor.
What you are missing is that the resistor increases the time constant and may in fact sligthy increase the release time compared to the case where the diode is included.
It is a complex situation. The initial voltage across the coil will be 12 Volt, not 11.3 as you have shown since, due to the coil inductance, the current does not change when the button is released.
In your second diagram, ie. where there is no diode, the voltage across the coil will be 12 Volt and the voltage across the resistor will be I * R where I is the coil current and R is the resistance of the resistor. For example, if the coil resistance is 600 Ohm, the current will be 12/0.6 = 20 mA.
If R = 82 Ohm, the voltage across it will be 20/1000 * 82 = 1.64 volt.