با آرزوی موفقیت

Yes, it's very respectful. However, 'Movaffaq bāshi' is more common for daily small tasks.

Only if they mention a specific challenge (like a big project). Otherwise, it's too formal for a romantic setting.

English 'Good Luck' can be used for gambling; Persian 'Movaffaqiyat' is almost always for earned success.

You can write it exactly as is, or use the shorthand 'Movaffaq bāshi'.

Yes, it has Arabic roots, but it is fully integrated into Persian grammar and usage.

It's better to use 'Khoshbakt bāshid' (Be happy/fortunate) for weddings.

The phrase is neutral, but you can add 'barāye shomā' (plural/formal) or 'barāye tō' (singular/informal).

No, it is a secular, professional phrase, though it can be made religious by adding 'Inshallah'.

No, use 'Bā ārezuye salāmati' (Wishing you health) instead.

There isn't a direct 'wish for failure' phrase used in polite society!

Yes, Tajiks use it, though they might also use 'Muvaaffaqiyat' with a slightly different accent.

For a trip, 'Safar-e khosh' (Happy travels) is better.

No, that just means 'Success'. You need the full phrase or 'Movaffaq bāshid'.

It's a voiced uvular stop, similar to the French 'r' but further back in the throat.