To call something impeccable is to emphasize its lack of flaws, faults, or blemishes, and to suggest that it is beyond reproach. Given that criteria, it’s no surprise that impeccable also connotes rarity and—drawing on its earliest sense in English, “not liable to sin; incapable of sin”—a degree of virtuousness. An impeccable reputation, for instance, is one untainted by scandal or intrigue, and impeccable credentials are so squeaky clean, they leave no room for objection or doubt.
A desire is a longing or craving for something. An appetite is also a desire or craving, especially for food or drink. But as a synonym for desire, appetite is usually more abstract, connoting a preference, eagerness, or taste for something intangible, such as power or adventure. In these cases, appetite is usually followed by the word for to indicate the object hungered after, as in the public's appetite for change, a company's appetite for risk, or, as the case may be, a synonym seeker’s insatiable appetite for learning!
The adjectives smart and astute both describe intelligence, which takes many different forms! Smart usually implies a quick or ready mind; astute connotes robust comprehension, marked by piercing insight and impressive discernment of detail. When used to describe people, astute also suggests shrewdness, cleverness, and cunning. Someone who is described as astute, such as an astute politician, is able to not only understand a highly nuanced situation in great detail, but also use that insight to their advantage.