Rule 1: 1. Two endings instead of three
An ordinary noun has three indefinite endings, ـٌ ـٍ ـًا. A diptote never takes tanwīn and has only two: ḍamma in the nominative and fatḥa in both the genitive and the accusative. So عُمَرُ is the subject form, and عُمَرَ serves after a preposition, after a noun in iḍāfa and as the object of a verb alike.
عُمَرُ فِي الْمَطْعَمِ.
ʿumaru fi-l-maṭʿami
Omar is in the restaurant.
Nominative: ḍamma, no tanwīn.
هٰذَا بَيْتُ عُمَرَ.
hādhā baytu ʿumara
This is Omar's house.
Genitive after a noun in iḍāfa: fatḥa.
رَأَيْتُ عُمَرَ فِي السُّوقِ.
raʾaytu ʿumara fi-s-sūqi
I saw Omar in the market.
Accusative: the same fatḥa.
عَلَى الْمَائِدَةِ مَلَاعِقُ وَسَكَاكِينُ.
ʿala-l-māʾidati malāʿiqu wa-sakākīnu
On the table are spoons and knives.
أَكَلْنَا فِي مَطَاعِمَ كَثِيرَةٍ.
akalnā fī maṭāʿima kathīratin
We ate in many restaurants.
The diptote takes fatḥa after فِي, but its adjective كَثِيرَةٍ is an ordinary word and keeps kasra and tanwīn.
اِشْتَرَتْ زَيْنَبُ فَوَاكِهَ لَذِيذَةً.
ishtarat zaynabu fawākiha ladhīdhatan
Zaynab bought delicious fruit.