Learn Italian: La dottoressa risponde gentilmente a qualche domanda. - The doctor kindly answers a few questions.

It is formed by taking the adjective gentile (kind) and adding the suffix -mente (which works just like "-ly" in English). Because gentile ends in an "e", you simply attach -mente directly to the end to make gentilmente (kindly).

Why is there an "a" after risponde?

In Italian, the verb rispondere (to answer or reply) is usually followed by the preposition a when you state what or who is being answered. It helps to think of it as saying "The doctor replies to a few questions."

Why is it qualche domanda (singular) when the translation says "a few questions" (plural)?

The word qualche means "some" or "a few", but it has a strict rule in Italian: it must always be followed by a singular noun. So, even though the meaning is plural in English, you must write qualche domanda rather than using the plural noun domande.

Does dottoressa just mean "doctor", or is it specifically female?

Dottoressa is specifically a female doctor. If the doctor were male, the sentence would use il dottore. Many professions in Italian have a specific feminine form, often created by adding the -essa ending.