Learn Farsi: از نظر ناخدا، این دریای متلاطم زیبا است. - From the perspective of the captain, this rough sea is beautiful.

Both translate to "in [someone's] opinion," but از نظر (literally "from the perspective of") is often used for a slightly more objective or formal statement of someone's viewpoint. به نظر (literally "to the view of") is very common for everyday subjective feelings, like saying "It seems to me..." (به نظرم).

The word for rough, متلاطم (motalâtem), seems very advanced. When exactly do we use it?

It is an evocative word meaning "turbulent," "stormy," or "choppy." While it is most literally used for describing crashing waves and rough water, at the B2 level and beyond, you will also see it used metaphorically to describe chaotic situations, such as a "turbulent market" or a "stormy political climate."

What is the rule for adding the explicit ی in دریای (daryâ-ye)?

This is a quick refresher for the Ezafe (the grammatical link between a noun and its adjective). Because the word دریا (daryâ, meaning "sea") ends in the long vowel alef, the Ezafe is pronounced as -ye rather than -e. In writing, this requires adding the explicit consonant letter ی to bridge the two words.

Can I use ناخدا (nâxodâ) for the captain of a football team or an airplane?

No, ناخدا is strictly a maritime and naval word, historically translating to "master of the ship" (from an old root for ship + خدا meaning master or lord). For a sports team or a commercial airline pilot, you would use the loanword (kâpitân).