Learn German: Vorsicht ist hier sehr wichtig. - Caution is very important here.

Just like in English ('Caution is...'), German often leaves out the article for abstract nouns when making a general statement or giving a broad warning.

Is Vorsicht feminine even though it doesn't end in -ung, -heit, -keit, or -schaft?

Yes, it is die Vorsicht. While it doesn't use the specific suffixes from this lesson, it is built from the prefix vor- and the noun Sicht (sight). Many nouns that are formed from a verb root plus a -t (like Sicht from sehen, or Fahrt from fahren) are feminine.

How could I turn the adjective wichtig from this sentence into the noun 'importance' using the rules from this lesson?

You can add the suffix -keit to create the noun Wichtigkeit (importance). Because it ends in -keit, you automatically know it is feminine: die Wichtigkeit.

Why doesn't the adjective wichtig have an ending here, like wichtige?

Because it comes after the verb ist (is) rather than directly in front of a noun. In German, adjectives only take on extra endings when they are placed right before the noun they describe (for example, eine wichtige Sache). When used on their own after a verb, they stay in their basic dictionary form.