Just do what the datasheet says, 10k 1% between NTC output and Vcc. The humidity sensor
output just goes to an analog pin direct.
This device consists of a humidity sensor chip (which is why it needs power) and a separate
NTC thermistor (a standard curve 10k one I suspect), which shares the same ground pin.
You have not shown how you want to connect the sensor. Thus, any answers are going to be a guess. A good starting point might be on page 6 of the data sheet.
You need to know your temperature range (if measuring temperature), the maximum resistance of the sensor over this range (if measuring temperature), the minimum resistance of the sensor over this range (if measuring temperature), the circuit, the voltage applied to the circuit, and whether you want to measure humidity, temperature, or both.
You probably want to stay well away from the values in the table called "MAXIMUM RATINGS". This means keeping the supply voltage, the maximum current and the maximum power well away from their maximum limits. I suggest starting at about half the limit.
Too much current (and thus power) will cause the temperature reading to be higher than expected because the sensor itself will heat up (aka self-heating).
So the original humidity controller DID have a separate temperature probe, but the funny thing is the controller didn't have any settings to control temp- I know on some sensors, there's an equation for calculating rH WITH the temp reading, but from my understanding and from looking at compensation equations for other sensors, it's mostly useful for high heat (perhaps also low) environments.
I am simply running a 5v wire to the sensor from the Arduino Mega's 5v out, bringing the data wire back to an analog-in port, and taking the other wire coming from the sensor to ground.
It is not a very good data sheet. I would have liked to see a suggested circuit diagram.
If you just want RH, you hook it up as you did, and no resistors are needed. Use the equations or table on page 3 of the data sheet. Be aware of the ADC resolution on the Mega.
I don't know what "In any power mode" means. Power modes are not discussed anywhere else that I can find.
Really the only tricky part here is the selection of the resistor ("RBATCH") for use with the temperature sensor, or more to the point, you're probably confused as to why they didn't just include one in the sensor to begin with. It's a bit hard to explain unless you play with the numbers in a spreadsheet and graph the results or such, but you're going to get the most precision if you choose a resistor that matches the resistance in the chart (page 5) for your target temperature. They suggest a 10K because the sensor is designed for room temperature (25C) and that's the most common use, but if you were going to use it in an application like an egg incubator (38C) then you'd want a use a 6.2K resistance.