4,320,000 years * 1000 = 4,32,00,00,000 years is 1 day of Brahma ...
First of all, as per the original verse found in Moksha Dharma Parva -- page 177 -- verse 20, there is no mention of "celestial years". Hence 1 cycle of 4 Yuga-s is 4800 + 3600 + 2400 + 1200 = 12000 years.
चत्वार्याहुः सहस्राणि वर्षाणां तत्कृतं युगम्।
तस्य तावच्छती संध्या संध्यांशश्च तथाविधः ।।२०।।
celestial years is the duration of the first or Krita age. The morning of that cycle consists of four hundred years and its evening is of four hundred years.
The Brahma's day is said to be sahastra such yuga cycles. Now Sanskrit word sahastra may mean "thousand" or "so many". But "so many" is subjective, it can mean anything less than or more than 1000. If we choose 1000, then the total duration of day/night will be 12000000 = 12 million years. So Brahma's full cycle will be 24 million years.
The learned say that these twelve thousand years constitute what is called a yuga. A thousand such yugas compose a single day of Brahman. The same is the duration of Brahman's night.
What do Lord Vishnu and Lord Shiva do after 1 Kalpa when Brahmadev goes to sleep ?
Since you haven't tagged your Qn as "mythology", I am answering this from regular perspective. Trinity of lords -- Brahma, Vishnu, Shiva (not Shankara), should be interpreted as supreme reality -- what is known as Brahman in Gita. This Brahman is said to be neither existent nor non-existent, yet immutable.
The relative "creation" & "destruction" happens during Brahman's day. However, during its night nothing remains. Gita doesn't use word "destroy" for this. It just uses "Avyakta" .. i.e. "unmanifest" or "inexpressible".
To answer your Qn: Absolutely nothing remains, this includes Brahman (trinity) itself. However to express this, the word Nirguna Brahman is used, which means "inexpressible". Everything merges back to the truest nature of Brahman, which is also called liberation (see the combined meaning of BG 9.7 & BG 14.2).
BG 8.17, 8.18, 8.19 - Knowing that thousand eras constitute a day of Brahman, [and] thousand eras complete a night, are the people who know day, [and] night. On arrival of day, all manifestations originate from "Unmanifest"; On arrival of night they annihilate into [what is] known as "Unmanifest" only. This [same] elementary world only happens again & again; Annihilates upon arrival of night, [and] originates upon arrival of day.
You may refer this anwser for further clarifications.