Learn German: Obwohl der Laie keinen Widerspruch geschickt hatte, prüften wir den Fall. - Although the layperson had sent no appeal, we checked the case.

If this sentence is the result of 'verbalization' (turning a prepositional phrase into a clause), what would the original noun-heavy sentence have looked like?

It would use the preposition trotz (despite) instead of the conjunction obwohl. A common way to phrase it would be: Trotz des fehlenden Widerspruchs des Laien prüften wir den Fall. The lesson teaches you how to turn these dense noun phrases back into more natural-sounding subordinate clauses like the one in our main sentence.

Why does the first clause use the Past Perfect (geschickt hatte) while the second uses the Simple Past (prüften)?

This highlights the exact sequence of events. The checking of the case happened in the past (prüften), but the opportunity for the layperson to send an appeal happened even earlier. Using the Past Perfect (Plusquamperfekt) for the earlier event and Simple Past (Präteritum) for the later event keeps the timeline perfectly clear.

Is der Laie a standard noun?

It is a 'weak noun' (an n-declension noun). This means it takes an -n ending in every case except the nominative singular. Because it is the subject here, it stays der Laie, but if it were the object, it would change (e.g., Wir fragten den Laien).

Does Widerspruch always translate to 'appeal'?

Not always. In everyday language, a Widerspruch is simply a 'contradiction' or 'disagreement.' However, in legal or administrative contexts, it is the specific term for a formal 'appeal' or 'objection.'