Hi Vijeth,
Let's start with your last question first and work backwards. Can you ever get zero result with the input at zero? There is the condition of noise and how it affects the result. Noise in the supply, noise in the ground, and noise of the reference must be considered. If you short the inputs (0V input) the output code will be close to zero, but with noise. How much noise will be dependent on the factors I just mentioned.
The Figure 9 in the datasheet has an OPA365 op amp in series with the input, so to get to ground (as the op amp can't drive all the way to ground) a pull-down is used.
When connecting the thermocouple, you could connect one end to ground, but you may see the effects of ground bounce ( or noise) on the signal. You might want to bias the thermocouple above ground.
Now to the first question. The ADS1112 always takes a differential measurement where one input is compared relative to the other. A pseudo differential measurement adjusts the measurement point above ground as the ADS1112 cannot measure below ground. If you make a single ended measurement relative to a voltage higher than ground (let's say 2.048V), the total measurement range is 4.096V instead of 2.048V when AIN- input is connected to ground. Anything above 2.048V is a positive code, and anything below 2.048V is a negative code. You can correct the result in software by adding the code value of 2.048V. The problem is the result is only as accurate as the stability of the 2.048V input.
Hope that helps,
Bob B