My question is, whether "Hiking" and "Cutting" are verbs, or a gerunds?
All gerunds are a subcategory of verb functions/forms, so the choice cannot be between gerund and verb, but between gerund and some other type of verb function/form, such as a participle.
...it really confuses me the fact that in my sentence the subject ("Interest rates") is followed by the preposition "to" which is used with verbs...
In English the preposition "to" in this usage can be freely used after both nouns and verbs, so you cannot use its presence to diagnose whether a verb form is a gerund or not. All of the following sentence are equivalent, although not equally idiomatic. Only the last example uses "hiking" as a gerund:
- The government is hiking rates to control inflation.
- The government is making rate hikes to control inflation.
- Rate hikes to control inflation are being made by the government.
- Hiking rates to control inflation is what the government is doing.
You could, of course, use "hiking" as a participle, and not as gerund. For example:
- This is a government hiking interest rates to control inflation.
You could even start the sentence with a participle phrase acting as an adverb, saying:
- Hiking interest rates to control inflation, the government will only push employment higher.
Although this last sentence is perfectly grammatical, it is not the best way to express things, since the semantic relationship between the participle phrase and the rest of the sentence is unclear and puts a large burden on the reader/listener to infer the relationship. If the semantics of such a phrase is not immediately resolved, it is more common to say something like:
While/Though hiking interest rates to control inflation, the government will only push employment higher.
Despite hiking interest rates to control inflation, the government will only push employment higher.
Notice that "hiking" is a participle used used to create an adverb clause in 7, but is a gerund used to create a noun phrase in 8, despite the same form. To prove this difference, note that you could rephrase 8 to say: "Despite the interest rate hikes to control inflation,..."; however, you could not rephrase 7 in this way.
The fact that the same form of verb can be used used with similar semantics, while creating different parts of speech, is one reason that gerunds can be confusing.