The adverb of lawful is lawfully.
An example sentence is: "he was lawfully arrested for the theft of the teabags".
lawfully
A derivative adverb would be the adverb form of a derivative adjective: one formed from a noun or a verb by the addition of a suffix (and possibly by a prefix as well). An example would be the adjective lawful (from the noun law) and the adverb lawfully.
Depending on its use, just can be either an adjective or adverb. just (adj.) - fair, lawful just (adv.) - right before, exactly, only
Adverb
Yes, thankfully we can use it as an adverb. It is the adverb form of the adjective thankful.
(You would have to use the adverb, which is tenderly.) She touched his face tenderly.
You would have to use one of the adverb forms "thoughtfully" or "thoughtlessly."
Formulaically is the adverb form of formula.
As an adverb .
no
Like this: I did my history homework yesterday. That's how you use yesterday as an adverb in a sentence
Adverb: I had a hat on. Preposition: I didn't have any money on me.
The adverb would be "inalienably." But it would have very limited use.