The present participle of "suppose" is "supposing."
Omnipresent
The word you are looking for is "ubiquitous."
It is an adverb, not a verb,; it can accompany a Present, a Past, a Present Perfect, a Past Perfect and a Future verb.
Unlike the case of split infinitives, I think it is acceptable to interpose the word always within the present perfect, e.g. "She has always been fond of chocolate." I checked one supposed English reference and saw this usage.
No, "always" is used to indicate that something is continuous or unchanging. Since the past tense implies that something has already happened and is completed, it would be contradictory to use past tense after "always."
always present means that you are always there.
He has the potential to be a great student. The potential for violence is always present.
It can be either it depends on the context of what you're saying.
Confidentce - it only can arise when you feel secure and it is always present in security.
You use the present continuous tense when you are trying to express that an action is happening now, in the near future, repetition and irritation with the word 'always'.
She took a quick glance at the clock before diving back into her work.