These words have similar meanings, so the relationship between them is that they are "synonyms". Synonyms are words with similar meanings, and they can often be used interchangeably within a sentence. Other relationships could include antonyms, which are words with opposite meanings.
In the sentence: "We would like to work in the soup kitchen <u>more frequently</u> next year", the degree of comparison of the underlined adverb is B. Comparative.
In English grammar, an adjective or adverb can be in a particular form that implicates a comparative relation. This relation can be of more or less, or greater or lesser.
Comparatives are characterized by the suffix -er ("This house is bigger than the other one") or distinguished by the word more or less ("This job is more difficult than the other one").
I believe this is a dependant clause