What type of thermocouple are you going to use ?
Referring to your original cicruit from post #1, it can't work, because the common mode voltage requirements are not met. AD620 isn't suited for single supply operation, you need a negative supply below the input common mode and output reference voltage, as the datasheet cicruit clarifies. INA121 is basically behaving similar. There are different example circuits in the datasheet and additional explanations, that clarify the requirements. The said circuit from post #6 simply says, that the TC input must not float. But it doesn't talk about supply voltages.
It's the measurement setup to determine the said characteristic. As a simplified result, you need dual supply with INA121 or AD620. Some instrumentation amplifiers are suited for single supply operation, e.g. AD623.Don't really understand the circuit in the middle of the left graph
It is not an op amp but an integrated amplifier, the gain is set by the resistor.
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