To connect minds, that is a matter of metaphysics, and could probably be done through some form intense training of the mind, to connect souls however, is much simpler, and can be far more dangerous, for both the emotional psyche, and the soul. Any time you have s3x with someone, you bind your soul to their's in some form, as it is written "a man will leave his parents, and be joined to his wife, and the two shall become one flesh". This is why s3x should be saved for marriage, if you are truly going to give all of yourself to your spouse, then you should not permanently bind yourself, body and soul, to someone else. To abuse this great power shown in the s3xual faculty, and bandy it about, only using it for pleasure, is a sin that reaches far beyond many others in terms of how displeasing it is in the eyes of God.
Human empathy comes closest to what you're asking. When we see, hear or are aware of the experiences of others, parts of our own brain become active as though we were experiencing the same thing. The idea of a telepathic connection has been lab tested and shown not to exist. There is also no evidence for the existence of a soul or spirit.
I used to work shift work and, if my relief didn't turn up at midnight I stayed on till morning. We didn't have a phone at the time so there was no way to let Daizy know I wasn't coming home. Then one night I fell off a train. I wasn't badly hurt but was kept in hospital overnight.
But Daizy woke at about the time I fell and sat up all night worrying. She'd never worried before, just that one night.
There have been other occasions.
It's possible to rationalise events like that, to explain them away, but when they continue to occur, no matter how infrequently, it's probably smarter to accept that there's something unusual involved.
Yes, I believe its possible, just one example in my experience has been while away at school I would get up from doing whatever.. And sit by the phone in Our Dorm Room just about a few seconds before the phone would ring and answer with Hi Ma! Freaked my roommate out first few times:-). Reverse held also, Ma would have same experience on her end. And no, we would not phone regularly or at any given time; International Phone lines from my country to the US were quite erratic.