Learn Italian: Di solito si risponde in modo gentile. - Usually, one answers in a kind way.

The si here is the impersonal 'si'. It translates to 'one', 'people in general', or the generic 'you' in English. So si risponde means 'one answers' or 'people answer', rather than referring to a specific he or she.

Why is risponde in the singular form?

When using the impersonal si without a direct object following it (like in this sentence, which only has an adverbial phrase), the verb is always conjugated in the third-person singular (the 'he/she/it' form).

Could I say gentilmente instead of in modo gentile?

Yes! in modo gentile translates to 'in a kind way', but you can absolutely use the adverb gentilmente (kindly or politely) instead. Italians use in modo plus an adjective very often as a natural alternative to adverbs ending in -mente.

Does di solito have to go at the beginning of the sentence?

It usually goes at the beginning to set the context, but it is flexible. You could also put it at the end and say Si risponde in modo gentile di solito and still be perfectly understood.