C, the result of their actions is that are banished from his garden and good graces
This is a participle. It cannot be a gerund, because gerunds have a nominal or adjectival meaning (for example, Swimming is fun - swimming would be a gerund). The -ing form itself is not a 'verb phrase', but 'sneezing uncontrollably' is. So if we are looking only at 'sneezing', the answer is 'participle'.
Lauren walked slowly, but Caroline walked quickly.
"But" is the conjunction, and "slowly" and "quickly" are the adverbs.
A because idk just guessing