TCA9617A: Pedestal and Inverted Pedestal of 9617A

"Would someone explain, in which two situations these pedestals occur as they are not alike? "
Figure 10 is the rising edge when B side is driving low but then releases (like if the I2C device/responder were on B side and ACK'ing or during a read transaction where it is sending data to the host), this pedestal is generated by the internal logic which requires A side to go above a threshold value before it can fully release and rise on B side. So if you drive from B side, you need to wait until A side goes above a voltage threshold when B side wants to release before it can fully rise. 

Figure 11 shows the fall time accelerator (when A side drives low while B side is high) which is a temporary pull down to GND before releasing to the offset voltage (this will remain until A side releases). This is done incase there is a heavy capacitive loading and to also speed up prop delays.

" Are they taken for different modes of I2C operations or they are the curves taken in the same operation mode but with different pull up resistors?"

No, they are just taken from different perspectives. Figure 10 is when B side is driving the low and releasing. Figure 11 is when A side is driving low. 

"In either case, the datasheet does not mention the setup environment. Please explain why are they different? "

The only set up difference is which side is driving. Pull ups and operating speed wouldn't change this.

"Another question, the pedestal and inverted pedestal in fig 8 are specifically shown with SDA and SCL lines, respectively. Is Pedestal associated to SDA and Inverted-Pedestal associated with SCL only?"

I like this question, it doesn't get asked very often. SCL is typically uni-directional so if you have an I2C host on A side and an I2C device/responder on B side, then the only pedestal type you see will be the one in figure 11. If we were to swap the host and responder, where the host sits on side B and the responder/device sits on side A, then you'll see figure 10's pedestal instead. 

SDA will have both pedastals at some point in the transaction though you will see one more than the other based on which side the host sits on (B or A) in regard with the I2C device/responder.

-Bobby