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“You know,” said Roark, “I haven’t thought of you at all. I thought of the house.” He added: “Perhaps that’s why I knew how to be considerate of you.” 

A great example of how a selfish desire can lead to altruism.

What does it mean for a sense of identity to integrate with the world?

Personally I hated the fountainhead, precisely because of quotes like this

The metaphor of every piece of land or person having the perfect house to match it undermines the subjective nature of our values

I actually started learning more in depth about objectivism as a sort of a hate-learn because I felt like I must be missing something

But no - it truly as it is - Ayn Rand believed there is an objectively best set of values for every individual, and we should all strive to meet our ideal

Even if we entertain the premise of her metaphysical argument on why existence "predates" consciousness, and therefore there must be a set of values that is objectively good, the subjective nature of our existence (our senses bodies and minds heavily altered under different physiological circumstances)
means we can never access this objective reality in an objective way

"Rational selfishness" is not the answer. Neither is sacrifice. A sense of identity that integrates the world with the self is