I chop my oats up in a coffee grinder but all sprinkle some bigger pieces on top. I don't add anything extra to it either. I add my oats to my oils and stickblend well.
Lemon juice will react with the lye and increase your superfat - if you're not experienced with adding acids to soap, I wouldn't necessarily mess with that.
I've used it in soap and in combination with a citrus fragrance, it was nice. I don't think it would be good to add to a soap with milk, though!
I wonder if she watched a particular youtube video (one of the first I watched when I was new) where this lady pours in a huge bottle of lemon juice into her soap. I won't link it, because her methods are not really very precise and she never mentions using a lye calculator. If you want to see it, search Homemade Soap at Marshas on youtube.
Yes- absolutely! I myself use baby oatmeal, which is probably even more instant than the instant shown in your link (it's very finely flaked- almost like fairy dust).