I've been unable to find any mention of Stewart of Parkbeg, or of Drumfurrich (I presume that Drumnaquirriche is a variation of Drumfurrich) in The Scots Peerage index, or The Heraldry of the Stewarts index so if those designations are correct then there don't appear to be any sources that confirm this Stewart line. Later profiles in this genealogy do have some sources, but I'm not totally convinced they are necessarily all from the same family.
AI is currently very poor at genealogy - there are no Earls of Castlemilk (AI must have picked this up from unsourced online genealogies). There are Stewarts of Castlemilk, perhaps Lairds of Castlemilk, and Baronets but that line became extinct in 1797.
