No on all counts as far as Isaiah's Call is concerned. The card says "While in battle...", meaning that unless he's in battle, those effects do not happen. They do not get to persist through the phase as normal, because he is not "in battle".
Abilities that don't have that wording, like Isaiah's protection of purple kings, do persist until the end of the phase they were active in unless they are negated (obviously cannot happen to Isaiah). Because it does not have stipulations like Call, Isaiah's ability itself would be able to persist.
Does that answer your question?
