No we are not property, but we can own property.
If my service is required to for you to to obtain your objective, can I claim a part of it.
Not unless it was part of the deal when you sold your services. You can not have a valid claim if it was not part of the deal.
If my service is essential for you to obtain your objective can I require you to surrender a portion of it to me?
This is where the market place comes into play, you can charge what ever you desire for your services, you could charge a million bucks an hour if you desire. It is up to other people to chooses to trade their property with you. You may risk pricing yourself out of the market.
This is aside from you hiring me from in front of Walmart.
What service are you selling in front of Walmart? I hope it is not a service explaining what ones Property Rights are, and why they are important.