There are Primal/Paleo mayo recipes. Google. I have not tried. A couple times a week, I'll have a tablespoon or two of real mayo. Not recommending, just saying.
Corn is technically not a vegetable. It is a grain. Paleo folks generally avoid. I have a couple organic corn tortillas every week. I would have more if I could handle the carbs. And I have some fresh, local corn every summer. Again, not recommending, just saying. If you have corn, make sure it is organic. Nearly everything else is GMO.