Learn Swedish: Vi pusslade på oförtröttligt hela natten. - We kept on doing the jigsaw puzzle tirelessly all night.

Adding the particle på gives the verb a "continuative aspect"—meaning the action just kept going. While vi pusslade simply means "we did the puzzle", vi pusslade på emphasizes that we kept on doing it continuously, much like saying "we puzzled away" or "kept on puzzling" in English.

When speaking this sentence, where should I put the stress in pusslade på?

As is standard with Swedish particle verbs, the stress falls heavily on the particle rather than the verb itself. You should emphasize på, making it sound like one connected unit: "pusslade-PÅ".

In English, the translation says "doing the jigsaw puzzle", but there is no word for "doing" in the Swedish sentence. Why?

In Swedish, you don't need a helper verb like att göra (to do) for this activity. Instead, the noun ett pussel (a puzzle) is turned directly into the verb att pussla (to put a puzzle together, or to "puzzle").

How is the long adverb oförtröttligt constructed?

It means "tirelessly" and is built from three parts: the negative prefix o- (un-/without), the root adjective förtröttlig (tiring/wearying), and the suffix -t, which turns the adjective into an adverb so it can describe how you kept puzzling.