خیلی مهم نیست

No, if you are responding to their apology for a minor mistake (like a typo on the board). However, don't use it to describe their homework assignment!

'Kheyli' adds a layer of politeness and emphasis, making it softer. 'Mohem nist' is more direct and can sometimes sound a bit blunt.

Yes, for minor things like a rescheduled meeting. For more formal issues, use 'مشکلی نیست' (moshkoli nist).

You change 'nist' to 'nabood': 'خیلی مهم نبود'.

Yes, though they might say 'Besyar mohem nist' more often, 'Kheyli' is widely understood.

If you say it with a cold tone, it becomes passive-aggressive. It's better to be honest or use a more formal 'I'm upset' if the situation is serious.

The most common slang is 'بیخیال' (Bi-khial) or 'ولش کن' (Velesh kon).

Not exactly. It's only 'You're welcome' in the specific context of someone saying 'Sorry.' If they say 'Thank you,' use 'Khahesh mikonam'.

Be careful. 'He is not very important' (Oon kheyli mohem nist) can be very insulting unless you are talking about a minor character in a story.

It is an Arabic loanword that is fully integrated into Persian.

Use 'خیلی خیلی مهمه' (Kheyli kheyli moheme) or 'حیاتی است' (Hayati ast - It is vital).

It's part of the culture of 'Gozasht' (forgiveness) and 'Ta'arof' (etiquette), aiming to keep social interactions pleasant.