Learn Finnish: Tämän ison hämähäkinverkon alla on vanha taskukello. - Under this big cobweb is an old pocket watch.

They are required by the postposition alla (under). In Finnish, postpositions force the entire noun phrase coming before them into the genitive case. So the basic phrase tämä iso hämähäkinverkko gets an -n added to every word.

Let's break down the word hämähäkinverkon. Why is there an -n- in the middle of it?

It is a compound word made of hämähäkki (spider) and verkko (web or net). The first part is in the genitive case (hämähäkin), making it literally a "spider's web". The very last -n at the end of the word is there because of the postposition alla.

Why does the sentence start with the location rather than the subject?

This is a classic existential sentence, used to express that something exists in a certain place. In Finnish, you usually put the location first (Tämän ison hämähäkinverkon alla), followed by the verb (on), and finally the thing that exists there (vanha taskukello).

This lesson is about the clitic -kohan. How would I use it here to say "I wonder if there is an old pocket watch under this big cobweb?"

You would attach it to the verb and move that verb to the very front of the sentence. The sentence would become Onkohan tämän ison hämähäkinverkon alla vanha taskukello? By combining the question clitic -ko and the wonder clitic -han, you turn the statement into a pondering question.