Can I re-summon an instance of a creature which has previously died within 24 hours?

Question

According to the Conjuration Magic rules (emphasis mine)

Summoning: a summoning spell instantly brings a creature or object to a place you designate. When the spell ends or is dispelled, a summoned creature is instantly sent back to where it came from, but a summoned object is not sent back unless the spell description specifically indicates this. A summoned creature also goes away if it is killed or if its hit points drop to 0 or lower, but it is not really dead. It takes 24 hours for the creature to reform, during which time it can't be summoned again.

However, when you Summon a creature, you do not Summon a particular creature, but rather a manifestation of that creature

Conjuration: Each conjuration spell belongs to one of five subschools. Conjurations transport creatures from another plane of existence to your plane (calling); create objects or effects on the spot (creation); heal (healing); bring manifestations of objects, creatures, or forms of energy to you (summoning); or transport creatures or objects over great distances (teleportation). Creatures you conjure usually- but not always- obey your commands

Does this mean that the 24-hour timer on death of a creature applies to:

1. A given creature (I can't summon the same Celestial Eagle twice in one day if the first one dies)
2. A given type of creature (I can't summon any more Celestial Eagles after the first one dies)
3. A given type of summon (I can't cast Summon Creature I twice in one day, if the first one dies)?

In both of the latter options, how does this rule interact with the secondary effects of high-level Summon Creature such as Summon Creature II?

This spell functions like summon monster I, except that you can summon one creature from the 2nd-level list or 1d3 creatures of the same kind from the 1st-level list.

My table has always played in a pretty unrestricted format in the regards to this, resulting in what is effectively the first option. We never consider a summoned creature to have any memory of previous events, and we allow the same type of summoned creature to be summoned repeatedly.

Answer 1

Yes

As the text on Conjuration (Summoning) says:

bring manifestations of objects, creatures, or forms of energy to you (summoning);

They are not real things, and while that specific manifestation might be wounded, stressed or even dying, you can simply summon another manifestation of the same type of creature using another spell.

In theory, each casting of Summon Monster conjures a different creature from the last, otherwise, it would be impossible to summon 1d3 creatures of the same type.

James Jacobs said:

On Golarion, if you use a calling spell to conjure an outsider, and then kill it, it dies as surely as if you killed it on its home plane. If you instead use a summon spell to conjure an outsider, the thing you summon isn't real before and after the summon spell ends. It doesn't "go back" to an outer plane when you kill it or dismiss it or the spell ends... it just stops existing, just as it didn't exist before you cast the spell in the first place.

But that's on Golarion, Paizo's Campaign Setting, and might or might not be true on other campaign settings.

So, where the summons come from, what happens to them, what they eat and their personalities are explicitly left open for each GM to decide how to handle these things.

Most people treat summons like creatures made out of magic, that only exist while the spell lasts, while others have their own ideas for their home campaigns.

The only known way to summon specific creatures is knowing their True Name (from Ultimate Magic). The rules for that, however, are a little mixed up between Calling and Summoning outsiders, as they give specific rules to enhance Calling spells, but nothing is given about Summon spells.

But we can assume that the general idea works for both subschools, as no exceptions were given to Summoning spells.

So, for a generic setting, we can assume that you cannot summon a specific creature again (say, Bob the Eagle), if it died while being summoned. But you can summon any other creature of that same type.

Rules as Intended

James Jacobs also said, later, on the same topic (yes, it's a long topic):

When you summon a creature using summon monster or summon natures ally, how does it work? Does it conjure a likeness of that creature to fight for you or does it bring a real creature from somewhere?

It summons a "copy" of an idealized incarnation of the creature. A summoned creature doesn't exist before you cast the spell, nor does it exist once the spell expires.

That's the difference between summoning spells and calling spells. Calling spells DO conjure a real creature.

Note that, this time, he did not refer to Golarion when answering the question. Although he could be talking about Golarion when answering this. But this means that the intent of the spell is that you create a creature made of magic using summon spells, not real creatures.

So, even knowing the true name of a creature, it cannot be summoned with Summon Monster.