Not sure where to begin with the rest of this!
First of all, can we tell on the 1861 census for William and Elizabeth Murray whether William is the LODGER or the HEAD? Would be very strange if Elizabeth is the daughter of him and Judan that she would be listed as the Lodger's daughter if William is not the lodger - would make me think that he is not the real father.
I too think it possible that Juda was a Scotch interpretation of an Irish Judy, and highly likely that McCall was not her real maiden name - leading me to believe that it is something close like McCann or McCabe, or to believe that they were not married at the time.
It is perhaps telling how little the descendents know of these people - my wife's uncle, who was a very intelligent man interested in his family history, was only 4 when his grandfather Patrick John died but remembered the events and knew the entire history of his life - but when I asked him about Patrick's parents, he said that his father had not known anything other than the fact that his grandfather was Irish. So perhaps there was a reason they did not speak of it.
There are also a large number of coincidences here. Elizabeth Knox reported the death of Judan the criminal - Patrick John married a Catherine Knox. Judan later married a Thomas Hughes - and we have the link to a Patrick living as a lodger with a Hughes in 1851. There was a Patrick McCall who married a Catherine McCabe in 1851, and I looked hard at that union as a possibility but they had children throughout the 1850's. I know that these are common names in the area at the time, but still interesting to see the names come up again and again.
The answer would have to lie in the 1851, 1861, or 1871 census data - by 1881 Patrick John was likely in Rhodesia, which is why he does not appear, and in 1891 and 1901 he is in Blackburn.
I have no idea what to do with all of these theories!! You are much better detectives than I am!