like "He", "His", "Thy", "the Creator", "the Omnipotent", etc.
What is the origin of this practice? When should I capitalise words like this? for any deity? only the deity of the Abrahamic faiths?
There are sort of two categories here- your first three examples are pronouns, while the latter two are epithets. Traditionally, epithets are capitalized for any individual, be they god, godess, Greek hero, or office worker. Epithets are grand titles that go beyond mere descriptive phrases, standing in for the name of the individual. For instance, an epic might start using "Father of Waters" any place it would name Poseidon.
Capitalizing pronouns is a bit different- from the best of my observations, pronouns are only capitalized when referring to the Abrahamic deity, but it is simply a convention used to respect and set apart God, Jesus or the Holy Spirit from any other male that might be in the setting. It is certainly grammatically acceptable to leave any such pronouns in lowercase- indeed some translations of the Bible do this. It should be noted, however, that if you do so, you may confuse and quite honestly upset members of those faiths.