Life actually works like this: We are all free to do whatever we want. Seriously. We can do whatever we want, within the bounds of the physical world of course.

Well ... yes, I suppose you're right. To offer a crude example, I am free to approach that sweet young thing and have a lovely time enjoying her body, even if she doesn't find much interest in the enterprise, because I can. I'm bigger than her. I must, however, be willing to accept the consequences of my actions, which — in our utopia devoid of laws — can include being killed or severely injured by her or her friends if the activity was nonconsensual. This is where I part company with your answers to the next question.

What keeps us from pursuing this total freedom? Two things, I think: the desire most humans have to see ourselves and be seen by others as a good person; and our social nature (of which the first reason is a part).

I think you've underestimated the power of consequences. I enjoy my freedom; imposing on other people's freedom (such as the sweet young thing's freedom to choose her partners) may have an extremely adverse effect on my own freedom or even my life, and therefore I refrain from forcing the issue. I also would set an example that larger persons than I can consider themselves free to impose themselves physically on me. Far from wanting to be seen internally and externally as a good person, I am wary of what might happen if I act on my desires.

From this evolves what we've codified in the zero aggression principle and the proverbial Golden Rule. I am free to do whatever I want provided I don't infringe on your freedom to do whatever you want. A corollary is to treat others the way you'd like to be treated.

Do I have the "right" not to have my freedom infringed? Sure I do, if we agree on the code. But anyone can disregard the code anytime, and we each need to be on our guard.

You're correct in saying there's no such thing as rights, if there's no such thing as agreements between and among individuals. And other individuals can impose on your agreements at any time, so it's wise to "have at least a niggling awareness in every situation that my bubble could be burst."

I'm not quarreling loudly with your conclusions, which can be reached either through your premises or mine. My quibble is that I don't refrain from grabbing that sweet young thing because I want her to think I'm a nice guy. I keep my hands to myself so they (or some other part of my body) don't get cut off.
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"People should not be afraid of their governments. Governments should be afraid of their people."