Is it okay to drop my tip out beds at rest stops or Walmart?

If you pull in to a rest area, you can not encroach on another parking spot which looks pretty tough in your rig. I think you might be okay in a Walmart, but you need to go inside the store and talk to the manager to get permission. Explain what you're trying to do, let them know when you will be departing and the size of your rig. Be courteous no matter whether their response is positive or negative. Ask for specific instructions on where they want you to park, and make sure to patronize the store.