I can’t speak for pjen, but I’m guessing a farm egg is one bought direct from a farm, rather than a supermarket. Much fresher and probably free range rather than battery. (Also, all the eggs we get over here seem to be brown. Marketed thus a long time ago when there was the misconception that brown eggs were better for you. I haven’t seen a white egg here for years.)
Bubble and squeak is vaguely like hash browns but with other vegetables in it - usually left-over greens like cabbage and brussels sprouts, mixed with mashed potato and fried. An acquired taste but a damn good one.
Tattie scones are like flattened American biscuits, but made with potato in the dough too.
I am wishing that I was at pjen’s house this morning; brunch there sounds divine.