According to the Young Earth Creationism, how is the whole earth globe after the creation of the light?

This answer is based on a 2019 article Light Before the Sun: How biblical apologists have historically understood the source of light before the sun was created in Genesis 1 by authors speaking on behalf of a premier Young Earth Creationist institution: Answers in Genesis.

The article presents several Young Earth Creationist views that have been held in the past (along with their weaknesses) then presents Ken Ham's view as one possibility (Ken Ham is co-founder and CEO of Answers in Genesis):

• Tertullian (155-220 AD) : the light was a physical manifestation of Christ's glory in creation week, 4 millenia before the Incarnation, based on John 1:9
• Ephrem the Syrian (306-373 AD) : Pillar of fire that later became the sun
• Basil of Caesarea (329-379 AD) : God created the essence of the sun from days 1-3 and put it in the "lamp" of the sun on day 4, likening it to the burning bush (fire was not really burning from the bush)
• Augustine of Hippo (354-430 AD) : Angels as Luminaries provide the light (Job 38:7, Ps 104:4, Acts 12:7, Rev 12:9)
• Rabbinic Judaism view in Midrash Bereishit Rabbah (completed c. 500 AD) : God's Shekinah glory (Ex 40:34, 2 Chron 7:1-2, Eze 43:2, Ps 104:2)
• Matthew Poole (1624-1679 AD): bright cloud which moved across the earth, later repurposed as the sun on the 4th day
• Dr. John Whitcom (1924-2020 AD): proto-sun which was done away with once God created the sun on day 4
• Ken Ham (1951- AD): doesn't take a position, but states that it must be a light source which shone on a rotating earth once the light and darkness were separated to functionally serve the same purpose as the later-created sun

The article then states how Young Earth Creationists are open to multiple hypotheses:

As can be seen from the small sampling above, there are numerous views on this subject, and all of them are based on accepting the Bible as the ultimate authority and then using theological inference from Scripture alone to develop an explanation for that which Scripture does not specifically state. Ultimately, we must admit that Scripture doesn’t satisfy our curiosity on this question, but leaves us free to put forth possible explanations, as long as we acknowledge that we cannot dogmatically assert our favored hypothesis as “fact.”

The article concludes with several guidelines to forming a Biblical hypothesis:

• That the light is a created light from a source(s) that no longer exists
• That we shouldn't mix the prophetic language in Revelation to interpret historical narrative in Genesis
• That we shouldn't limit our understanding of how when God first created light, it lit up everything, recalling 2 Cor 4:6

Conclusion

Answering your question:

How is the whole earth globe after the creation of the light? Is the whole surface of the earth bright, or there is a part of its surface which is dark?

I think it's safe to say that the earth is already a rotating globe before Gen 1:3, and that the light shining on it came from heaven, which already exists since Gen 1:1. Like "a light from heaven shone around" Paul/Saul on the road to Damascus (Acts 9:3), this light can be from a physical heaven (i.e., sky) or from spiritual heaven (i.e. God's Throne Room).

Quotes from Chapter 8 of Ken Ham's 2016 book The New Answers Book 1: Over 25 Questions on Creation/Evolution and the Bible:

The first three days are written the same way as the next three. So if we let the language speak to us, all six days were ordinary earth days. . . . The sun is not needed for day and night. What is needed is light and a rotating earth. On the first day of creation, God made light (Genesis 1:3).

The phrase “evening and morning” certainly implies a rotating earth. Thus, if we have light from one direction, and a spinning earth, there can be day and night.

Some people ask why God did not tell us the source of this light. However, if God told us everything, we would have so many books we would not have time to read them. God has given us all the information we need to come to the right conclusions about the things that really matter.