Jisho

by getting used to spoken Japanese...?
just like the more you read the faster you get at reading

Both the singer and the female reporter voice actually speak quite slowly (or at least at a more relax speed) than standard everyday japanese.
The video is obviously really old, the audio is quite F*ked up so dont beat yourself up if you cant hear them.
I can hear a bit, he's talking about when his song started to get broadcasted nationwide and he got famous to the degree that he can hear his name randomly shout out on the street etc.
If you want to listen to fast spoken japanese, easiest to check out youtube short or tiktok (they HAVE TO talk fast over there xd)
And some of the shorts even have subtitle so it's a pretty good way to practice listening.
The TIP is that: Dont pay too much attention on individual words.
The fact about language all over the world is that natives never enunciate (i.e. properly pronounce) anything. So try to close your eyes, feel the pronunciation then compare what you hear to the subtitle, and find the shortcuts that they made.
For example: 正義を見た。looks like it should be pronounced like this "せいぎ　お　みた" but the O usually carries over to the previous word so natives would pronounce せいぎょ　みた or even せいご　みた.
If you dont know how fast (normal for natives) naturally spoken japanese typically sounds like, sometimes it's hard to find the correct one to practice listening. In most Anime and (many but not all) youtube videos, they enunciate (and slow down) quite a bit so it's not similar to normal natives conversation. My tip is to find contents where the natives speak WITH each other (as opposed to speaking to us the viewer), NON-SCRIPTED (at least partially), that's where their conversation is most natural.

Thank you for the beautiful explanation! It helped me! Really. A lot.!!
But how do I get the script of what is being spoken? Usually, natural conversations are not scripted, but to read and comprehend them it would be better to get their script. And you also mentioned the term improper pronunciation of native speakers of the language. It sometimes becomes very hard to listen. How do I comprehend it after numerous listening to that particular phrase/sentence?　
Last time I also created a discussion about
"What does 「頭があるそうないざに絡まれる」mean?"
After I made Google translate hear it I got it.
It was actually「頭が悪そうなユーザーに絡まれる」
Same problem again
In this video clip (https://youtu.be/Leiebo4V2cE?si=nAkPLEPaodC6_e-t)
The anchor said　「恋に終止符をうち、北へ帰る女の悲しい心情、見事なまでに謡いあげた名曲　津軽海峡冬景色。この○○○○は石川さゆりさんです。」
Again the same problem comes.
Here（https://youtu.be/81uuwkzjtfk?si=h4CMQLAJ4Bvdkza5）3:04
Anchor says(夏から秋への海鳴りに見知らぬ街が飛んで行く、あなた訪ねて一人なり。もの静かな北陸地方さゆり演歌に○○○○出来ない謡いなのです。能登半島)
I marked the as the words which I could not hear. I ask help from you to kindly make these words clear to me.
Thank you for your support and dedication towards me through this beautiful response.

I marked the words as ○○○○which I could not comprehend.

Let's address the clip first. It was hard to hear for me too so I'm glad I finally got it to give you the answer ^.
In the first clip, he said 「このコーナーを締めくくりは石川さゆりさんです。」 "The final song (to end this segment of the TV program) will be from Ms Ishikawa Sayuri".
コーナー is a counter for TV program (segment) and newspaper segment. This stems from the literal newsPAPER where you have each sections/corners of the paper telling a different news story, and then it becomes the word for each timeslot of TV program too.
In the second clip, he said 「さゆり演歌に欠くことが出来ない」 "the beautiful singing that the northern land couldnt live without"
There's a common pronunciation pattern in both of these clips. That is the pronunciation of the く. when they shorten it, it sounds like the small っ , しめくくり⇒しめっくり ；かくこと⇒かっこと。
About the script, so far unfortunately the clips that fall within the bound of your interests doesnt seem to offer much subtitle. But clips surrounding japanese pop culture/memes do have subtitles. Even in natural conversation, they would add subtitles (in BOLD too xd) to emphasize.
For the clips above, I tried listening to it repeatly, but it didnt help much. I also tried to slow down the video but it still didnt help. The only thing that helped me figure out was the context. The first clip when i heard コーナー i already suspect that she has something to do with maybe "perform in this segment". The second clip, the context also kinda tells you that the people of that area really like her singing.
So, context is supremely important. In psychology, they'd tell you that your brain fills in the gap where you wasnt able to hear if you already know the context. I know that this doesnt help you figuring out an actionable plan to improve other than keep immersing yourself and practice, but that's really it. I usually cant hear 100% what people say, but if the context helps me understand the conversation well enough, that's an absolute win xd.

I see. I learned a lot of new things. Oh, I feel that I am the king of the world. I am so happy that I was being assisted by someone in the field of my keen interest. Everyone would criticize me that is why I am killing my time. But you helped me a lot. Thank you for teaching me many valuable lessons. ご回答有難う御座います。

Glad I can help ^. I just like explaining things that I know, and I love japanese language, so I hang out in this forum all the time xd. Good Luck for whatever you want to do!

Thank you very much!! My gratitude from the bottom of my heart!!