Learn Farsi: آیا بیمه‌نامه‌ی پزشکی هنوز معتبر است؟ - Is the medical insurance policy still valid?

It is a very useful compound word combining bime (insurance) and nāme (letter or document). You will see the -nāme ending on many official documents in Farsi, such as gozarnāme (passport) or gavāhināme (driver's license).

Why is there a "ye" sound in bime-nāme-ye pezeshki?

That is the ezafe connecting the noun (insurance policy) to its adjective (medical). Because bime-nāme ends in a silent "h" (ه) that sounds like "e", Farsi inserts a "y" sound (written as ی) to bridge the gap smoothly. It is pronounced bime-nāme-ye.

I know pezeshk means "doctor". How does it mean "medical" here?

By adding the very common suffix -i (ی) to the end of a noun, you can turn it into a descriptive adjective. Here, adding it to pezeshk (doctor or physician) creates pezeshki, which means "medical" or "related to medicine".

Do I always have to use āyā (آیا) to ask a yes/no question like this?

Not always! In everyday spoken Farsi, people often drop āyā entirely. You can just say the sentence like a normal statement but raise your pitch at the end to show it is a question. āyā is mostly used in writing or slightly more formal speech to clearly mark a question from the very first word.