Circuit turn on delay question
To get the relay to delay start as you want, you need to have it connected across the capacitor in your diagram.

As you say, the freewheeling diode then becomes irrelevant.
To get the relay to switch, the resistance used to charge the caps needs to be low enough that the equilibrium point eventually reached is high enough to put enough current into the relay coil to close. That then determines the size of the (bank of ) capacitor(s) you need for the appropriate timing. D2 also becomes irrelevant, since there's no path for it to discharge through, the relay coil current is the only thing that discharges the cap.

I have a few soft start boards (used with big SMPS and toroidal transformers) that work like this, the bulk and cost of the caps (on the left) means that a simple circuit with a low current charging cap and a transistor driving the relay would probably be a better choice.