Decide coherent time and fade duration through empirical studies on the channel and relate them to channel modeling
You're only observing power transmission, not phase - where I come from, we care about that just as much, so coherency would incorporate phase and amplitude of the channel coefficients just as well.

Anyway, if the phase of your channel impulse response doesn't matter to your application, then these measurements are OK.


  
  Can I assume 3 minutes to be the coherent time of the channel?
  


You definitely can't say your coherence time is three minutes.

There's significant jumps that happen between measurement points, for example around 3 minutes, 6 minutes, 9 minutes...

So, we can even say that the coherence time is smaller than 30s, and your measurement isn't fine enough in time domain to even measure that.

The channel is a result of its environment. If there's movement in your medium, and movement in your transmitter, you'll need to measure "often" relative to the amount of time it takes for movement to achieve a displacement in the order of one wavelength. f = 500 MHz = 5 · 10⁸ Hz leads to a wavelength of \$\lambda=\frac cf=\frac{3\cdot10^8}{5\cdot 10^8}\,\text m=60 \,\text{cm}\$; let's say you'd at least want to look whenever something moves a tenth of that, i.e. 6cm. (realistically, a channel measurement would try to look > 100 times per wavelength of movement, rule of thumb, but 10% does sound like a start)

You don't mention relative movement speeds, but let's roll with 1 m/s. Then, 6cm of movement would take 0.06 s, which is way, way less than the 30s you're measuring, but still larger than the coherence times we observe in microwave indoor communications (e.g. WiFi, but that has significantly smaller wavelengths, too!).


  Can I assume the no-signal period to be fade duration?


no, because that could just be a random observation; your observation is too seldom to say whether the channel is "good" in between.


  How to model the channel when the TX-RX distance was not stable? Can I develop a model for the changes of received signal against time?


Model path loss as function of time, and model fast movement as Doppler shift if necessary. Use the common methods of describing channels through coherence time, doppler spread, delay spread. Continuously measure channel impulse response rather than just sporadically look at a power transmission coefficient.