2. I do (as someone mentioned above) have a grandfathered unlimited data plan and I do NOT have "WiFi hotspot" included as an add-on to my Verizon plan; however, that never stopped my Moto X v2 and Moto X Pure Edition from having a working WiFi Hotspot right out of the box. Having the WiFi hotspot option blocked is new (to me) with the Pixel and it seems odd that going from a phone made by Motorolla which was mostly "pure" to one made by Google (both on the same carrier) would actually cause me to lose my free WiFi Hotspot. I didn't make any changes to my actual Verizon plan when I purchased the Pixel or when my wife picked up her new SIM.
Agree with @lunatic59. It's well known that grandfathered unlimited plans don't get tethering/hotspot by default. Even when unlimited plans were offered, hotspot was an additional feature. You can no longer add that feature to your plan even if you have a granfathered unlimited plan. Welcome to the trade off of keeping your unlimited plan in an age of data buckets. I'm sorry, this is probably not something you were hoping to read