Congratulations to you for finding the Primal Blueprint. You sound like you're ready to make the commitment, and a trip to the grocery store is a great way to start.
About the dairy question: Whole dairy is just that, completely whole. No fat removed. Whole dairy = full-fat dairy, preferably organic, no hormones, grass fed is the best but harder to find. You'll find differing opinions about whether dairy is primal. Whether Grok ate dairy or not, I don't really care. I'm not too hung up on re-enacting the Paleo era, and try to concentrate more on erasing as many "civilized" industrial agricultural era components from my diet as possible, especially grains and processed foods. Whole dairy helps me in my attempt to increase the fat ratios in my diet, so I include heavy cream, butter, and cheese. I believe that a person's ability to consume dairy without harmful side effects is directly correlated to their ancestry. Northern Europeans/Scandinavians have a very low rate of lactose intolerance, so if you fall within that ancestry you should be okay. Also, dairy consumption is very helpful to former vegetarians who are transitioning into primal eating. You may also find it helpful to include lots of free range eggs in your daily eating.
I'm sure others will come along with their take on your questions. Good luck!