How long would we live without the sun

The Sun is expected to become a red giant in about five billion years. It is calculated that the Sun will become sufficiently large to engulf the current orbits of some of the solar system's inner planets, including Earth.[6][7][8] However, the gravitational pull of the Sun will have weakened by then due to its loss of mass, and all planets but Mercury will escape to a wider orbit. That said, Earth's biosphere will be destroyed as the Sun gets brighter while its hydrogen supply becomes depleted. The extra solar energy will cause the oceans to evaporate to space, causing Earth's atmosphere to become temporarily similar to that of Venus, before its atmosphere also gets driven off into space.[9] Venus will become a burnt out planet; its atmosphere having long been driven off, and its rock will melt.[1]

I was trying to come up with a solution to the timeline when hypothetically speaking the sun would stop shining ( or emitting radiation). Now, gravitational issues aside (the sun as a body still there), how long would it take for median temperature to drop beyond freezing point around the globe? How long would it take for the oceans to completely freeze, and how long would it take for the air to become liquid or solid?
I'm wondering if anybody did a research on this topic, I searched the internet but could not find anything about the subject.

Also, as the sun burning hydrogen in its core it becomes more efficient, therefore, gets hotter (as I understand). Somewhere I saw that it increasing its output about 10% in billion years. How long would animals have left on this planet, and how would it affect us humans in.... let's say 10,000-50,000 years from now.
Thank you very much

do you think the earth would change its orbit as the sun becomes red giant, or would it be engulfed by the "surface" of the sun altogether?

In a couple of billions of years, the oceans will start boiling, and that is when the life on Earth will end, do not worry about the Sun exploding in 4 billion years, life as we know it will end in 2

yea. it is true but we wont live to see it though. maybe scientist have found a way to this problem by then. but do you know that the earth itself is already dieing? changes may happen!
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Assume earth is a black body radiator, calculate rate of energy loss. Multiply the latent heat of freezing water by the seven oceans.

How exactly is the Earth dying? Do you mean that its rotation is gradualy stopping, or that the Moon is getting farther away? Or the Global warming? Or do you mean the tsunamis? or 2012?