Learn Portuguese (Portugal): A rapariga ficou na margem, observando a boia. - The girl stayed on the bank, observing the float.

In European Portuguese, continuous actions usually use estar a plus the infinitive. However, when we want to express a secondary action happening at the exact same time as the main verb, we use the gerund (-ndo form). Here, observando acts as an adverb, showing what she was doing while she stayed on the bank.

Could ficou and observando be working together as a compound verb?

No, they are separate here. While ficar followed by a gerund can sometimes mean to keep doing something, the comma and the phrase na margem split them up. The verb ficou is the main action meaning she stayed, and observando is the simultaneous background action.

Why does on the bank translate to na margem rather than sobre a margem?

While sobre means physically on top of a surface, em (which combines with a to make na) is the most natural preposition to use for being at a geographic location like a riverbank, beach, or edge. We say na margem just like we say na praia for at the beach.

I have seen the word for float or buoy spelled as bóia before. Is boia a typo?