Learn Finnish: Tuskin olin huokaissut helpotuksesta, kun kömpelö koirani pudotti maljakon. - I had barely sighed with relief when my clumsy dog dropped the vase.

This is a classic narrative sequence. Tuskin (barely) pairs with the pluperfect tense olin huokaissut (I had sighed) to describe an action that was just completed. This is immediately followed by kun (when) and a simple past tense verb pudotti (dropped) to introduce the sudden interrupting event.

Why is "helpotuksesta" in the elative (-sta) case?

In Finnish, physical reactions or emotional responses are often paired with the elative case to express what caused them. Just like you might cry from joy (itkeä ilosta), you sigh out of relief, so helpotus (relief) takes the -sta ending.

Could I use the verb "putosi" instead of "pudotti" here?

No, because pudottaa (past tense pudotti) is a transitive verb, meaning someone actively drops a specific object. If you used the intransitive verb pudota (past tense putosi), it would mean the vase fell on its own, and you couldn't use the dog as the active subject.

Why does the object "maljakon" end in -n rather than being in the partitive case?

The dog dropping the vase is a complete, sudden action that affects the entire object. Because the action was seen through to the end, the total object takes the genitive-looking accusative ending -n instead of the partitive case.