چشم از چیزی برنداشتن

Yes, it is neutral to polite. It's not rude like 'staring' (zol zadan).

Absolutely. You can use it for a beautiful view, a movie, or a suspicious package.

'خیره شدن' is just the physical act of staring. 'چشم برنداشتن' implies a reason—either you're captivated or you're being careful.

Say: 'Nemitoonestam cheshm azash bardaram.'

Yes, to show you are monitoring a situation closely, like the stock market or a project.

Yes: 'چشم ازت برنمی‌دارم' (I won't take my eyes off you).

In Sufi poetry, it refers to keeping one's focus on the Divine, but in daily life, it's secular.

Just use the positive: 'بالاخره چشم ازش برداشتم' (I finally looked away from it).

Very common, especially when flirting or talking about a gripping TV show.

In Persian, we almost always use the singular 'cheshm' for this idiom, even though we have two eyes.

Not at all. It's used by all ages.

Using the wrong preposition 'be' instead of 'az'.

No, it is strictly for visual attention.

Yes, 'ghofl kardan' (to lock) is the modern slang equivalent.