Learn Hardcore Italian: Il cortile interno del palazzo è pieno di fiori in primavera. - The building’s inner courtyard is full of flowers in spring.

In Italian è (with a grave accent) is the third‐person singular of essere (“to be”). Without the accent, e simply means “and.” So here è tells you “is”:
Il cortile interno del palazzo è pieno…
= The inner courtyard of the building is full…

Why is interno placed after cortile instead of before it?

In Italian most descriptive adjectives follow the noun. Cortile interno literally means “courtyard internal/inner.” Putting interno after the noun is the neutral, most common word order. Placing an adjective before the noun can add emphasis or a poetic tone, but here you want the normal descriptive structure:
noun → adjective (cortile → interno).

What is del in del palazzo? Why not di il palazzo?

Del is the contraction of di + il. In speech and writing Italian typically contracts prepositions plus definite articles:
di + il → del
di + lo → dello
di + la → della
di + l’ → dell’, etc.
So del palazzo simply means “of the building.”

Why is it pieno di fiori and not pieno dei fiori?

When pieno (“full”) indicates that something contains an indefinite amount of something else, you use di without the article:
pieno di fiori = full of flowers (some flowers, in general)
If you said pieno dei fiori, it would imply a specific set of flowers you both know about (e.g. “full of the flowers [we saw earlier]”), which is less common here.

What part of speech is pieno and does it agree in gender/number?

Pieno is an adjective meaning “full.” It must agree with the noun it describes:
– sing. masc. = pieno
– sing. fem. = piena
– pl. masc. = pieni
– pl. fem. = piene
Here it agrees with cortile (masculine singular), so you use pieno.

Why do we say in primavera for “in spring” instead of a primavera or using an article?

Italian uses in + season without an article to express “in [the] spring, summer, autumn, winter.” So:
in primavera, in estate, in autunno, in inverno.
Using a primavera would sound odd. Also you don’t add la; you simply say in primavera.

Can palazzo mean just any building, or does it imply a palace?

Palazzo most often means “palace” or “mansion,” but it’s also used for large, elegant buildings or historical structures. In everyday speech il palazzo can refer to an apartment building or any sizable edifice, depending on context. Here it’s the main building whose inner courtyard you’re describing.

Could I say durante la primavera instead of in primavera, and what’s the nuance?

Yes, you could say durante la primavera, which literally means “during the spring.” It’s grammatically correct, but in primavera is more idiomatic and concise when simply stating that something occurs in that season. Use durante if you want to emphasize the time span more explicitly.