Does on the "Global rom" version every app will work normally?
This question is not that simple, and answer on it changes with the time and device you are asking about, so it's best to ask about concrete device using contact form on product page "ask a question"
Overall answer is:
For most of the Global rom devices like Asus, Oneplus, Nubia, Motorola everything should work fine - for some - Xiaomi - not everything. Financial applications can not fully work on Xiaomi, as they require device to be locked. Due to the Global rom installation process, Xiaomi devices need to be unlocked first. Applications like Google Pay will detect that device is unlocked. You may still apply patch to make such applications work after unlocking, but it requires some technical knowledge - we can sent you manual for most popular applications. Another way to get financial applications work is revert your device to it's original rom.