The section on attunement is quite long, so I won't reproduce it here, but it refers exclusively to a "creature". It doesn't say anything about a player, a player character, a humanoid, or anything else that would exclude familiars from being able to attune to magic items.
The ring of spell storing itself likewise has no restriction beyond requiring attunement, so yes, a familiar can attune to it. I feel compelled to point out that some DMs might not allow a pseudodragon to use a ring because it doesn't have fingers, though.
As for concentration, the DMG says this about items that cast spells (on page 141):
The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration.
So if you cast a spell into the ring that requires concentration, when your familiar uses the ring to cast it, your familiar will have to maintain concentration, not you.
Spells cast from the ring use normal actions and no components.
Many magic items allow the user to cast spells. The general rules for this are on p. 141 of the DMG, under the Spells subsection of Activating an Item:
Some magic items allow the user to cast a spell from the item. The spell is cast at the lowest possible spell level, doesn't expend any of the user's spell slots, and requires no components, unless the item's description says otherwise. The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration.
(emphases mine).
Beyond these rules for magic items, casting a spell follows the rules in the Player's Handbook; generally, the character casting the spell takes the Cast a Spell action on their turn.
Here's what the Ring of Spell Storing says about casting the spells in it (DMG, p. 192:
While wearing this ring, you can cast any spell stored in it. 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.
Let's look at two examples of stored spells being cast:
- Fireball stored in the ring at 3rd level by a 10th Level School of Evocation wizard with a save DC of 16
- Magic Circle stored in the ring at 5th level by a 11th level Cleric with a save DC of 17.
Fireball, cast from the ring by a 3rd level Sorcerer (save DC 14):
- Will require one action to cast (same as the spell)
- Will do 8D6 damage; the original casting wizard's Empowered Evocation feature will not apply since it is not one of the characteristics that the ring lists as being 'stored'.
- Can be used with Quickened Spell by the casting sorcerer, since that falls under being "treated as if you cast the spell".
- Will have a save DC of 16, from the original caster.
Magic Circle, cast from the ring by a 19th level Fighter:
- Will require one minute to cast (same as the spell).
- Will not require any chalk or other material components, even though that is normally required.
- Will have a duration of three hours (base duration plus two extra hours for using a 5th level slot).
- The fighter has no spellcasting ability, and thus no spell save DC, but the Magic Circle will have a save DC of 17.
Best Answer
It's not clear how stored spells should work with situational bonuses
The Ring of Spell Storing states:
So we need to determine what are considered to be your spell save DC and your spell attack bonus.
Your spell attack modifier is defined as follows (from the wizard class and the chapter on Spellcasting):
Note, it does not say that situational pluses and minuses change your attack bonus. Thus, it would seem that Rod of the Pact Keeper does not impact your attack bonus; instead, it gives you a bonus to your attacks, similar to the bless spell.
Meanwhile, your spell save DC is defined (from the same places) as follow:
In this case, the general rule actually does mention that special modifiers impact the actual save DC value. And while I do think it would be unusual to have the Rod of the Pact Keeper affect the save DC of stored spells but not their attack bonus, that is how it seems to be written.
A GM can always rule however they like
A GM is well within their rights to say that the Rod of the Pact Keeper applies to both your attack bonus and save DC or even that it applies to neither. They should probably keep in mind that this would mean any other situational modifiers (for example, from the resurrection, raise dead, temple of the gods, bless, and synaptic strike spells) similarly would or would not apply to stored spells.