What does nurturing do? takes time and resources. So for blank 1, we can consider that if the dealer want to nurture painters, they have to give their time and resources.
in blank 2, we should ask ourselves the question that why would a dealer not be patient with the young modern painter? because the dealer does not have the time and resources for it.
If a dealer can wait for a young painter to grow, it would be said he was patient/magnanimous.
Insatiable means tough to satisfy and quirky means unusual, which does not really fit into the context of passage.
A demand for modern art can be insatiable/ tough to satisfy. Hence, option C is the right answer.