Does a direct hit of missile on the target is simulated in Volkhov/Dvina, without use of proximity fuse?

No

With Volkhov, I had several situations over Hanoi where I had to fire the missile with "rabota ot K3" switch activated because of that nasty chaff layer, and with range boresight placed farther than the target actually was, and missiles did hit their targets. I could only explain this as a direct hit.

That is a program bug.
K3 should detonate when the missile reaches the range boresight.

Reloading the Volkhov/Dvina in combat conditions. What are exactly the criteria for initiating the reloading? With me, sometimes it starts, but sometimes not. I guess it had something to do not only with "gotovit" switch (to which position it should be placed, by the way, for reloading?), but with some other switches, too. What is the proper procedure?

It depends on the GOTOVIT switch.
3 will prepare - 3
6 will prepare - 6
N will start reload after launch (takes some time) until stock is exhausted.