2024 New Year in 2024

TIn three hours later, in my (local) time zone, I will enter the new year of| will enter 2024.

Let's [give a simple conclusion into | draw a simple conclusion for] the past year and share expectations for the coming one.

Although, ideally, the perfect date shwould behave been in August.

Nonetheless, I succeeded. here, thanks…

H…here, thanks to a church leader in Britain,(,) who has (regularly) spoken with me (regularly,) every two weeks, encouraging and praying for me.

Your original sentence was incomplete—it lacked a main verb. I fixed it by merging it with the previous sentence.

Furthermore, on the last day of 2023, I saw Lady Mari again on this website, who has encouraged me to keep on writing although I am really not skilled in / at it.

In the coming new year of| In 2024., I can…

I hope I can [figure out all the possible matters | sort out everything that comes my way] in 2024.

I am so grateful to everyone who has spent time reading and proofreading my non-native and unon-natural entries,. I understand it was a hard task for you.

The 2024 New Year in 2024

This sounds more natural. I'm not certain why, but I think it is because 'New Year' is coming up and is a one-time event, so it should be 'The'. It does not need 'in' because it is obvious that it will be in 2024. I hope this helps.

Three hours later iIn my (local) time zone, I willwe'll be entering the new year of 2024in three hours.

You don't need to say 'local' here, again it is obvious from context. However, because you are talking about something as big as a 'time zone' (which affects the whole country!) you do need to say 'we'. I contracted 'we will' to 'we'll' to make it read better, as well as changing 'will enter' to 'be entering'. 'Be entering' is used because it makes the event feel more imminent.
See:
It'll happen soon. - Will happen at some point in the future
It'll be happening soon. - Will happen at some point in the very near future.
I hope this makes sense!

In the coming new year of 2024year,/...

Again, obvious from context, so you can omit/remove the year.

I can anticipate I will face more unexpected challenges and experience some hard matters, however, moments of joy and exciting news will also come to me.

Great work!!! :)

I hope I can figure out all the possible matters inof 2024.

"I hope I can work through the difficulties of 2024."
"I hope I can endure the challenges of 2024."

Sounds better here.

'Figure out' does not seem right here. It is used for when you use logic and reasoning to overcome a challenge, and reads awkwardly when you are talking about challenges which may not require your head!
In English, the word 'endure', or 'work through', can be used for challenges/difficulties which do not always require intelligence/smarts. For things like sadness, bad news, financial difficulty. The idea is that you cannot 'fix' them, so you must 'put up/endure' with them.

When reading your passage, to me 'matters' is the difficulties you may face during the year, so it does not make sense entirely.

For example:
I hope I can figure out this maths problem!
I will be able to endure this sadness.
Can you figure out that puzzle?

???I don't know if I can figure out this sadness.
???I won't be able to endure this maths problem!

A good attempt though!

I am so grateful to everyone who has spent time reading and proof-reading my non-native and unon-natural entries, I understand it was a hard task for you.

Not at all! Your writing is fantastic :)

You said 'non-native' and 'unnatural' in the same sentence. They both mean the same, so you can get rid of one, as it reads funny.