Answer:
A. Securely
B. "...no way in the world can you get rid of the nasty hard thing..."
Explanation:
A. The word fast in this context means securely. For example, if I held my money fast it would mean that I clutched it tightly to make sure nothing could happen to it.
B. This quotation shows that the harness was held securely on the horse, since he couldn't get it off.
Participles are verb forms which look like verbs + suffix -ing. So having that in mind, the participle in the sentence above is the word standing.
Participles function either as adverbs (when they modify verbs), or as adjectives (when they modify nouns). In this case, the participle acts as an adjective, modifying the word child.