Haltingly is an adverb.
http://www.merriam-webster.com/dictionary/haltingly
She speaks haltingly because of her English accent
Speaking haltingly is the bad habit which can lead to decrease our ability.
An adverb is a word which modifies a verb, such as: She haltingly spoke of her experience. In this sentence, the word "haltingly" is the adverb. In the sentence you provided, "How" is not an adverb.
gradually, calmly, haltingly.
part of speech
The part of speech for this particular word is a noun.
The part of speech for "answer" is a noun.
adverb
what part of speech is beneath
The part of speech for "explicit" is an adjective.
The part of speech for "twirl" is a verb.