How to understand mosfet capacitance characteristics?
Brian Drummond's comment nailed it, but I thought it was worthwhile to expand on it to fully answer both of your questions.


From what I understand, Ciss = Cgs + Cgd with Cds shorted. So how can Ciss in the graph then vary as a function of Vds if Cds is shorted? Vds should by definition be 0V.

First, I want to clarify what you're talking about.  You referenced the Infineon Power MOSFET App Note in one of the comments, which states: \$C_{iss} = C_{GS} + C_{GD}, \text{ } C_{DS} \text{ shorted}\$
You can also find the same condition stated in Vishay/Siliconix datasheets, like in this chart for the SiHF10N40D:

This is quite vague, but the best clarification I found for what they mean by this can be seen in this article under Figure 4 (duplicated below).  Typical measurement equipment contains a capacitance (\$C_{BT3}\$ in this case) which snuffs out the \$C_{DS}\$ of the MOSFET while making the \$C_{iss}\$ measurement.  Like Brian mentioned, this &quot;AC shorts&quot; the drain and source while the \$V_{DS}\$ DC bias can still be swept.



It seems for the graph Vgs is fixed at 0V. How then does the f=1MHz come into play? Which voltage is alternating and with which amplitude?

Sounds like you might be unfamiliar with C-V measurements.  A small signal AC voltage (usually in the range 10mV to 100mV) is applied at different DC biases to characterize the non-linear capacitance of various semiconductor devices.  A good introduction can be found here, courtesy of Tektronix/Keithley.  The important thing to understand is that the AC voltage is small enough to assume linear measurement principles are valid.
Looking at both this app note by Tektronix and this one by Vishay, it appears the typical measurement of \$C_{iss}\$ is done by applying the AC voltage at the drain (while sweeping \$V_{DS}\$) and reading the AC current at the gate.  They both mention a frequency of 1MHz and if you look close enough at the screenshots, the Tektronix one shows an AC test voltage of 30mV.