That's good to hear that you have levemir, I think I was thinking of another cat who was on R insulin. The lev vials are about 280-400 a piece depending on where you get them, so that's something.
As far as home care, if your cat stops eating and drinking, or becomes weak take him in to the 24 hour vet as low potassium can lead to fatal weakness of muscles including the heart. I would definitely have them recheck the potassium level about 7 days after that last test to see if your supplement needs to be increased. That test should really be no more than about $30. If you are still not in the normal range, you need to ask about increasing the supplement. Also, try to feed a high calorie diet to get those ketones to go away (IAMS max cal, wellness pates, kitten food), you might need to increase insulin if you do this, that's a good thing. The ketones that he has means he needs the extra food and insulin because he's burned off some fat stores.
Otherwise, as far as the labs go, the only other things off are the eosinophils, WBC and platelets. It's common for platelets to increase in infection. Seeing his labs doesn't shout cancer in my brain. In cancer, cbc labs are usually very wonky (increased potassium, decreased platelets, decreased HgB, decreased RBC), all that looks pretty normal. Typical infections - UTI, respiratory (cats are prone to viral and fungal resp infections), bowel infections, pancreatitis flare, skin infections, parasites. The eosinophils actually help narrow that down - as these become elevated in bowel, parasite, or allergic issues. Flagyl is the antibiotic of choice for GI infections, but you'd probably want to get an x-ray to rule out blockage too.
Is your cat an indoor/outdoor cat? Do you live in the south or in a hot climate? Has your cat had fleas recently? Any issues with skin/fur?