Learn Polish: Trudno szacować straty po burzy. - It is difficult to estimate the losses after a storm.

In Polish, when you make a general, impersonal statement without a specific noun as the subject (like "It is difficult to do something"), you must use the adverb form (trudno) alongside the infinitive verb. You would only use the adjective trudne if it were describing a specific neuter noun, like To zadanie jest trudne (This task is difficult).

Why does the sentence use the imperfective verb szacować instead of the perfective oszacować?

Using the imperfective szacować emphasizes the ongoing or general difficulty of the estimation process itself. If we used the perfective oszacować, it would focus slightly more on the difficulty of completing the task and successfully arriving at a final number.

What case is burzy and what is its base dictionary form?

The base form is the feminine noun burza (storm). It is in the locative case here because it follows the preposition po (when meaning "after"). Feminine nouns ending in a "soft" or "hardened" consonant like -rza take the -y ending in the locative case.

How could we add the emphatic particle aż from this lesson to express shock at the number of storms?