Salàm, It's not very common to use "نهارك سعيد" to greet people in the morning. The most common way to do that is by saying "صبـاح الخـيـر"

No, actually we not use this sentence at all.. We say نهارك سعيد or نهار سعيد سيد.... ( اسم شخص Name ) Good evening

It's a classical Arabic :) We don't use it anymore. If you want to great someone in the morning, you can simply say " Sabah elkhir " صباح الخير However, it's fantastic to know that phrase it will make you better than the other learners :) keep in your mind that " in learning Arabic, The more you know the more you feel you don't know " Best wishes :)

سَعِيدَةُ مُبَارَكَةٍ

السلام عليكم