روز خوبی داشته باشید

Yes, it is perfectly appropriate and shows good manners. Just ensure you use the plural 'bashid'.

Yes, it's actually best in the morning or early afternoon because it wishes them a good day *ahead*.

'Ruz bekheyr' is more of a greeting (Hello), while 'Ruz-e khubi dashte bashid' is strictly a farewell (Goodbye).

You don't *have* to, but most people do. It's like saying 'Goodbye, have a nice day!'

Not exactly a slang version, but friends might just say 'Khosh bashi' (Be happy/well).

Because it's a wish. Persian uses the subjunctive mood for things that haven't happened yet or are desired.

Yes! Since 'bashid' is already plural, it works for one person (polite) or many people.

Yes, though the pronunciation and spelling (Рӯзи хуш) differ slightly.

You can still say it! It's a wish for their well-being, not a weather report.

It might be a bit stiff at the very end of a date. 'Khosh gozasht' (I had a good time) is better.

You can write 'Ruz-e khubi dashte bashi' or even use emojis like ☀️👋.

In this context, yes. It can also mean 'well' or 'fine' in other sentences.

Yes! 'Ghashang' means beautiful. It's a very nice, slightly more poetic variation.

No, it is a secular phrase, which is why it's so popular in modern, diverse settings.