Can a god be real and not omnipresent?
1. If by your definition, the earth, countries, users on RF are "real" , then they are real and not omnipresent.
2. If on the other hand by real you mean satya, sat -- then these examples above are neither real as in Satya nor omnipresent.
The highest Supreme is omnipresent, omniscient ...
Let us take 'a' god as you suggest - the Wind god VAyu, or the fire god Agni.
Is vAyu (gaseous state rep) omnipresent ? Present as far as the bounds of material universe - yes , but also in potential form after the dissolution of the univers
If Agni - fire omnipresent ? present as far as the bounds of material universe, because it is in potent form in places and at times it is not manifest as fire. e.g. fire is embedded in potential form in the wood or fuel, although it is not yet manifest. So Agni can be taken beyond universe into the potential of muLa prakruti.
Since these are parts and aspects of the Supreme Divine, Brahman, this does not apply completely to Brahman, only partially.
Brahman is
--immanent
--transcendant
--omnipresent
--eternal (sat - eternal truth)
--asat (transient states - that undergo transformation , universe etc. exist on the foundation of Brahman)
--neither sat nor asat (muLa prakruti)