That... might actually hinge on something else. One of the fairly major conceptions of th'christian/monotheist god I've seen in theological discussion is that it's... more or less atemporal (or more accurately, I guess, outside temporality), or perhaps omnitemporal (at all times simultaneously).
Change wouldn't be possible for that sort of being in the sense it is for a human, or at the very least wouldn't occur in a means we'd recognize. Vagueing it up a bit, it's hard to see exactly how change would work for a entity for whom all time is one time, its (more or less) present. Would that sort of thing even have a framework for past/future/change? From our perspective, though, almost definitely not -- all interactions with the divine would be with the exact same entity, regardless of temporal positioning from our side of things.
Alternatively, there may be no guarantee you're ever dealing with a sequentially aligned entity -- the god of the old testament might actually be a future entity, from the perspective of the God, and there would be no particular assurance that the entity you interacted with tomorrow wouldn't be radically different from the one today. I've not actually seen that put forward by a religiously aligned theologian, but it'd definitely be a possibility. S'interesting stuff, really.
E: That said, I imagine the more lay understanding would be that god could learn, but has no need to, as you mentioned. No reason, as all the decisions or knowledge god could wish to make or have is already known to god, so the general stuff that prompts humans toward learning or changing opinion simply isn't there.
As for change... maybe. From what I understand, that's somewhat underpinning the difference between new and old testament. Though it might be arguable that god did not change, merely the covenant god has with man, or whatever that is. Exactly where a person falls on it probably differs between denominations and religions, assuming they've ever really thought about it at all.