Learn Portuguese (Portugal): Controlada a inundação, o resgate terminou com sucesso. - With the flood controlled, the rescue ended successfully.

This is an absolute participle clause. It is a concise way to express time or cause without using a conjunction like quando (when) or depois de (after). You can think of it as a shortened, more elegant version of Depois de a inundação ser controlada (After the flood was controlled).

Why is the participle feminine (Controlada) instead of the default masculine (Controlado)?

In absolute participle clauses, the past participle acts like an adjective and must agree in gender and number with its own subject. Since a inundação is a feminine singular noun, the participle becomes Controlada. This is different from compound perfect tenses (like tinha controlado), where the participle never changes.

Why does the participle come before the noun here? Could I say A inundação controlada?

In Portuguese absolute participle clauses, it is standard and much more natural to place the participle before its subject. Saying A inundação controlada sounds like a simple noun phrase (the controlled flood) rather than a standalone action clause (Once the flood was controlled).

Why translate successfully as com sucesso? Is there a single adverb for this?

Portuguese often prefers prepositional phrases like com sucesso (with success) over adverbs ending in -mente. Be careful not to guess the adverb as sucessivamente! That is a false friend meaning consecutively or in succession, not successfully.