1. No one answered the ad but me.
Answer:
preposition
Step-by-step explanation:
In the sentence "No one answered the ad but me", the word" but" is a preposition meaning "with the exception of; except".
cf. "No one answered the ad except me."
2. There is but one choice to make in this case.
Answer:
adverb
Step-by-step explanation:
In the sentence "There is but one choice to make in this case", the word but is an adverb meaning "only".
cf. "There is only one choice to make in this case."