Yes Algia is another word for pain
Both are correct.
Synonym means: a word having the same or nearly the same meaning as another in the language. Definition means: the act of defining or making definite, distinct, or clear / the formal statement of the...
He is a pronoun. The only synonym it has is to use the name of the person it refers to, i.e., "He is short." "John is short."
Normally one would not use, or need to use another word. However, if your sentence is "God is." then the alternative would be "God exists."