Short answer: questions contain hidden complexity and words with multiple interpretations.

Long answer:

• You are free to enter into an agreement to meet at the pub that is non-binding, unilaterally severable, has no damages because there is no consideration specified, or for one of several other reasons will not get the police involved. You are also free to enter into a contract where, for instance, you and your friend will meet at the pub today and you will buy a round for the pair, and tomorrow you and your friend will meet at the pub and he will buy a round for the pair, and in that case I expect you could involve the police if your friend fails to perform. Perhaps I'm reading too much into single words when I read your "agree" and respond with a contrast between "agreement" and "contract", but I think there's a relevant point here about the amount of binding-ness and expectation involved and to what extent one is willing to be compelled by a contract one signs, because "agree to meet at the pub" conveys to me a sense of general intent, which has less force and fewer sanctions (social, legal, or otherwise) for violations than "promise to meet at the pub" which in turn is weaker than "contract to meet at the pub".
• In America, I would lean towards answering yes, with significant caveats about how "relationship" is to be interpreted. I refer you to the Diosdado case, where a man and a woman got married with some concern about the possibility of adultery, and therefore entered into a contract imposing certain penalties (a monetary fine; and to be considered at fault in an eventual divorce) upon an eventual adulterous party. Then one party committed adultery and convinced the court to throw the contract out of court in favor of granting a no-fault divorce and ending the marriage at no cost (except that paid to the lawyers). To make an analogy, the precedent here is that you can't be free to have monogamous relationship any more than you can free to have an abusive relationship, because any such relationship rests on an illusory promise (general term for promises of the form "I promise to do X if I feel like it", which have no force, and don't function as promises) as the counterparty can terminate it without warning, without cause, and without penalty. American courts don't expect an abused person to remain abused, and the American courts don't expect a married person to remain faithful, regardless of what either person signed.
• I would say you're free to be on a diet in that case.

Tapping out.