"Lovlig," or "Legal," is the adjective version of the word. To make Danish adjectives into adverbs, you would add a "-t" suffix to the end of the word (lovligt), similarly to how you would add a "-ly" suffix to the end of an English adjective to accomplish the same thing. This is covered more thoroughly in the Adverbs section.
I thing "wedding" mostly refers to the ceremony, and "marriage" refers to the legal (or illegal) granting of marital status to a couple. So for example, in states where same-sex marriage is against the law, two woman can have a wedding, which would be legal, but their marriage would not be recognized legally.