The scratching/scraping/digging movements round food bowls are basically instinctive efforts to hide their leftovers
one of mine does it, I think it's very sweet - if there's any newspaper down anywhere sometimes she will actually cover her food with it, but normally she just kind of shuffles it all around a bit.
I wouldn't pick Barney up at all, for now - lots of treats, lots of friendly talking, lots of 'distance' play (eg things on strings, feathers on the end of a wand and so on), gradually tempt him onto your lap with treats and toys, take it all very slowly and gently. Get him very used to and comfortable with your touch before you try to restrain him at all (which is what picking up is, if you look at it from the kitten's point of view). If they're alone during the day leave the telly or a radio on so there isn't a huge contrast between the silence when you're out and the noise when you come home.
Mine both had diarrhoea for about six days after they came home, I think it's fairly common, as long as they're eating and drinking well I think it'd be a good idea to stick to one sort of food for a bit - in small meals - and just watch to make sure they're not actually poorly in any way. If it doesn't stop after a week or so then it's definitely time to see the vet, ditto if they seem at all unwell.
Well done for taking these little chaps on - I'm sure they'll settle very soon and I hope you enjoy many many years with them.