Summons will activate more easily on the first stagger you perform or when your opponent's life drops to 1/4 or your life drops to 3/4, there will be no restrictions like your enemy's life drops below half.
You will also be able to summon in any phase of the Bosses and you will be able to Summon any entity you want in any battle (for example you can summon Shiva against Shiva, Leviathan against Abzu, etc... ).
You can summon the entities 999 times during a battle (if you can hehehehe....).

If you have used the Kingdom Save Editor to acquire the Ramuh Materia with Cloud you can always summon him, the only flaw is that the summon cinematic will not be seen but everything else will work correctly until the Final Special Attack cinematic.

All these effects only work in the battles that can be summoned normally, not where they are restricted (for example, you will not be able to summon Shephirot, 3 Whispers first phases, etc...)

I leave the duration of the invocations to your choice, you have three options and they can be used regardless of whether you use the previous MOD:

Summon Infinite Time: Summon lasts infinite time
Summon Instant Special Attack: The entity will perform the special attack as soon as it is summoned and will leave
Summon Time x3: Summon lasts three times the original time
Summon Time Halved: Summon time is halved to the original time