Although this will seem at first glance to be a bold statement, the answer to these questions is actually remarkably simple: it's all in how you define sentience. That is, the necessary and sufficient conditions for sentience would be precisely as they are defined. I think what people really want to know—in fact what they might have meant to ask in the first place—is "how would one measure X in another entity?", X being sentience, consciousness, whether it can actually feel pain/love/happiness/sadness, etc. That's where the real challenge lies. This touches on ideas like Solipsism, Searle's Chinese Room Argument, and the mind-body problem in general. But when you are asking for the conditions which make X, you are simply asking for the definition of X; i.e. that which makes X distinct from everything else.
In this case, the necessary and sufficient conditions for sentience are (depending on how you define "sentient"):
Sentience is the ability to feel, perceive or be conscious, or to have
Conscious or aware; Experiencing sensation or feeling.
Having sense perception; conscious; experiencing sensation or feeling.
–The Free Dictionary
- having the power of perception by the senses; conscious.
- characterized by sensation and consciousness.