Question: There is something about the derivation of the formula for parallel resistors I can not understand($1/R\_t=1/R\_1+\cdots+1/R\_N$).

1. In order to derive this formula we use that the potential is the same no matter which road the current takes.
2. That the potential is the same follows from Coloumbs law from charges with an electrostatic field. By integrating the force from Coloumbs law we see that the force is conservative.
3. So before we derive the formula $1/R\_t=1/R\_1+\cdots+1/R\_N$ we need to have established that the field is electrostatic?

What exactly is it that makes the field electrostatic? What is it for instance the prevents us from having current depending on time, and also a non-static field?

Answer: 
All the ends of the parallel resistors are joined at the ends so you have one common point -it does not matter if it is just one point or a wire without resistant-. So all points are at the same potential on one side, the same at the other side. This has nothing to do with conservative or electrostatic, they are also at every moment on the same potential if one has AC.
It does not matter wich point you take for potential 0, easiest would be at one end of your resistors. Than the Potential on the other side is defined by the work you need to transport a charge to this side divided by the magnitude of the charge. A wire or a conductor is supposed to not have a resistance, so the work along it ist 0. The potential on it ist the same at every point. This is the case with the wire which connects your transistors. For your parallel resistors only the voltage i.e. the potential difference matters, and of cause it changes, if you have AC, but in any moment you have a determined voltage. It makes no sense here to speak of a conservative field. To speak of a circuit and resistors in it, you have to have a source with a given potential difference. So what is really your problem?