A creature with a spell-like ability limited by "per day" uses will regain that ability 1 day from the time it used it last. As for spells they work the same as the class of which they are casting from; I.E. A cleric will pray to his god at a specific time each day and a sorcerer needs 8 hours rest and 15 minutes in meditation to get them back.

For your more complicated question about 3/day abilities and it only used 1 of its charges then that charge would refresh after 1 day or 24 hours from when it was used however if it used say 1 charge in the morning and 1 charge in the afternoon and 1 charge in the evening they would all return after 1 day from the last time it was used not the first time.

It is also a loose theory in that all spells don't really set by day but rather 8 hours of rest and 15 minutes to an hour of meditation... By that rule the per day uses would not recover until the creature had 8 hours of uninterrupted rest and then at least 15 minutes to refresh the daily uses of his Spell-Like abilities.

For book reference the best description comes from the Rules Compendium for Spell-Like Abilities stating them to be akin to the Bard or Sorcerer non-prepared spells, which is as follows;

Players Handbook I: page 178

> Prepared Spell Retention: Once a wizard prepares a spell, it remains
> in her mind as a nearly cast spell until she uses the prescribed
> "effort" to complete and trigger it or until she abandons it. Upon the
> casting of a spell, the spell's energy is expended and purged from the
> character, leaving her feeling a little tired. Certain other events,
> such as the effects of magic items or special attack from monsters,
> can wipe a prepared spell from a character's mind.

Recent Casting Limit:  page 179

> As with wizards, any spells cast within the last 8 hours count against
> the sorcerer's or bard's daily limit.

Spell-Like Abilities: Tome of Magic page 113

> Although you do not prepare spells, you must rest for 8 hours and
> meditate for 15 minutes each day to regain your use of mysteries just
> as a sorcerer or bard must rest and meditate to regain use of spell
> slots.

Mysteries are spell-like abilities FYI.

Spell-Like Abilities: Tome of Magic page 139

> Spell-Like abilities are magical and work just like spells (although
> they are not spells and so have no verbal, somatic, material, focus,
> or XP components). They do not function in an antimagic field and are
> subject to spell resistance if the spell the ability resembles or
> duplicates would be subject to spell resistance.