Learn Danish: Forsikringen giver fuld dækning. - The insurance gives full coverage.

fuld is describing the noun dækning, which is a common gender (en) word. If it were describing a neuter (et) word, it would be fuldt, and if it were plural or in a definite phrase, it would be fulde.

Does fuld mean "drunk" here?

No. While fuld is the most common word for "drunk" in everyday Danish, it also translates directly to "full" or "complete." The context of dækning (coverage) makes it clear we mean "full coverage."

Both forsikringen and dækning end in an "-ing" sound. How do I know whether to spell these nouns with -ing or -ning?

These nouns are formed from the verbs forsikre (to insure) and dække (to cover). Typically, you add -ning to the verb stem to make a noun (like dæk becoming dækning). But if the verb stem ends in a complex consonant combination like "-kr", "-dr", or "-kl" (as in forsikr), you just add -ing to make it easier to pronounce.

Could I just use the verb form and say that the insurance covers fully?

Yes, you could say Forsikringen dækker fuldt ud (The insurance covers fully). However, using the noun phrase giver fuld dækning is a very standard and professional way to express this in Danish, much like saying "provides full coverage" in English.