Assumption of SINR measurement
How can we measure the SINR of the nodes: as we do not have the Power x Gain product without the knowledge of Power and Gain of IoT nodes.


Not at all, you have zero information about the N in SINR, and without channel knowledge you also can't have any information on the S, nor the I, even if you knew the transmit powers (which you don't).


  Is it right to assume that the receiver of the AP won't be able to get any legible data (information) unless the SINR is above a certain threshold?


Yes. If you're into NOMA, you should be aware of a bit of basic information theory (otherwise, it's hard to understand why you'd even ever want to go non-orthogonal):

In this case, a very basic corner case of the Shannon Limit holds true. Some call it the ultimate Shannon Limit, but what it really just says is that if your bit energy is below -1.59 dB of the energy of your redundancy, you can't get any information from your reception.

In a multi-user system, one can (often iteratively) gain information about the interference¹, but if noise² alone pushes the SINR below -1.59 dB, you've lost and better redesign your system.


 ¹Thus reducing restoring the receiver's ability to "remove" parts of the entropy the interferer adds to the received signal.

²"Noise" actually being all entropy in the reception that doesn't come from the information source. That incorporates all entropy of interference that you can't "cancel", however that happens.