Yes. This does happen. The odd fish does stray or get lost and this is how Nature populates new rivers and streams. The vast majority however return to the natal stream. Theory is now backed up by science, with DNA sampling confirming the above.
Sure thing. And fish resulting from our own past stocking efforts. As a teenager through to my early twenties, then again in my thirties, I knew a man who had not only caught more British salmon than anybody, from the two Borders, from Scots and from Welsh rivers, by foul means and fair, rod, net, gaff, snare etc etc, but who also handled many many many tens of thousands of salmon as a "redchestered" (his boyhood Nith Country version of "registered") salmon dealer buying from anyone and sending them for sale to old Billingsgate, who could tell the provenance of a salmon at glance - "That's one of the old longer thinner fish from the Wye ... that's a Norwegian / Tweed / German fish put in by the old hatcheries ... that's original western Welsh ... whilst this nineteen-pounder of yours, Paul, is much shorter and deeper and probably in from the Solent, whilst this fourteen of mine is an Irish visitor....".
I am still inclined to believe him, though he has been gone since the 1980s (heart attack whilst pulling in a legal seine net in a Welsh estuary). Wish I had questioned him more, but as the bailiffs were always looking out for him on the rivers that we fished, it was best not to be seen talking with him for very long.