It does seem kind of intentionally-vague. I suppose that's so the DM and players can determine how much wackiness they want to inject into the campaign. Perhaps there will be more guidance for this in the DMG, when it comes out.

Like most things that are left up to DM discretion, this is something that the DM and players should discuss ahead of time, preferably before anybody rolls up a wild magic sorcerer. It's important that the player knows what the rules are, even if they're totally arbitrary.

Some options that would make sense to me:

1. Roll after every spell cast
2. Roll for a surge only when the sorcerer is under stress somehow
3. Roll for a surge only when it's potentially important to the story

Rolling for surges after every spell cast seems a bit extreme to me, given the chance of a TPK for some of those results, especially for a group of low-level characters. On the other hand, the really nasty results are a small chance, on top of the small chance of surging in the first place, so unless you had two unlucky rolls in a row...

I like the second and third versions, especially if you can work them into the character's background and personality. Maybe they're more-likely to surge when someone they care about is being threatened, or when their hit points are low, or whenever they're affected by a condition.

Based on the wording there, I would be inclined to say that it cannot wild surge when cast from storage unless the wild mage is also the one casting it from storage.

The spell uses the slot level, spell save DC, spell attack bonus, and spellcasting ability of the original caster, but is otherwise treated as if you cast the spell

This doesn't mention wild magic as one of the things that's retained from the original caster, so if someone other than the wild mage used the spell there would be no surge. If the wild mage is the one to use the stored spell, since it is treated as them casting the spell for everything not explicitly listed, I'd say there's a chance for a surge.

As for storing the spell, it says that the spell has no effect, but the description of the Wild Magic Surge feature says

Immediately after you cast a sorcerer spell of 1st level or higher, the DM can have you roll a d20. If you roll a 1, roll on the Wild Magic Surge table to create a random magical effect.

This strongly suggests that the wild magic effect is not part of the spell itself, as it happens after your cast the spell. In particular, no wild surge effect modifies the spell that triggered it. So it seems fair to say that storing the spell can trigger a surge.