In brief, is it permissible to greet disbelievers with a handshake, and what is the method for returning a disbeliever's greeting, and how does one greet someone whose religious state is unknown, and what is the ruling on a man shaking hands with and kissing his maternal aunt's sisters?

The ruling on initiating greetings with disbelievers and shaking hands with them has been clarified in previous fatwas. The general principle is that whoever is in Muslim lands and appears to be Muslim is considered Muslim, and therefore one should greet them with "Salam." However, if one is in disbeliever lands or they appear to be disbelievers, then it is most likely that they are disbelievers. In such cases, the ruling on initiating "Salam" with them is as explained in the aforementioned fatwas. There is no harm for sisters to greet their mother's maternal uncle by touching and kissing his hand, as long as it is not done with lust. If it is customary to kiss the hand of an elder mahram, then there is no objection to it.