If you know the current through one resistor in a DC circuit then do you know the current through all the other resistors?

No. Current and voltage are directly proportional to one-another and both are related to resistance by Ohm's law:

V = IR

or

Volts = Current * Resistance

So the current will depend upon the voltage and the circuit resistance by rearranging the above equations:

I = V/R

Meaning that the current will decrease as circuit resistance is increased if the voltage remains constant.