What are the supplications that God answers without delay, and what is the ruling on saying: "immediately, not later" in supplication, bearing in mind that the questioner is persistent in supplication and hopes for her need to be fulfilled in these days?

There is no objection for the supplicant to say in his supplication: "immediately, not delayed," as was narrated from the Prophet, peace and blessings be upon him. There are no specific supplications for immediate response, but desperation, persistence, presence of heart, and certainty of response are signs of an impending response. It might be better for the servant if the response is delayed or not granted, for Allah Almighty says: "But perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows while you know not."