why are the resistors marked in ohms. if they resist volts
Georg Simon Ohm told us that they resist the flow of current; they don't resist the voltage across them.
Resistors could be marked as voltage/current just as 1 mA meter movements [1 mA = a full scale reading] used in VOMs are marked as 1000 Ω/volt, but there are an infinite number of volts/amp combinations that could represent one ohm, and the VOM meter movements might take 0.4 v across them for a full-scale reading.
E = IR so 9 v/10 kΩ = 0.9 mA of current.
9v/1.6 MΩ = 5.6 µA.
In analyzing your circuit I would first assume that when the transistor is fully "on", looking into the base lead you see 1 v across each PN junction, which gives 2 v.
2 v across 470 kΩ gives 4.3 µA.
Assuming the base current is >10x less than this value the current through the 10 kΩ resistor and the water is also 4.3 µA.
(9-2)/ (4.3 µA) = 1.6 MΩ.
For this circuit more precision isn't necessary; if it was I'd also need to know the V I curve for your audible indicator, BUZ, and the current gain, β, at the currents of interest, of your Darlington pair, .
If this circuit will see temperature extremes or voltages down to 7 v or you would want to make many of these, you may need to know the range of these values more precisely, or replace the 470 kΩ resistor with a pot.