I had no idea at all about the show so far.

The main character's who is a chef in the drama is Kaoru Kobayashi, a very calm and cool actor.

I had no idea at all so farbefore then.

The main character's chef in the drama is the chef Kaoru Kobayashi, played by a very calm and cool actor.

He should be givinggives a nuanced performance.

He should be giving aprobably gave a very nuanced performance to the show.

This entry has already been well corrected by others, but I just wanted to offer an additional opinion on this line.

"Should" can mean "probably" or "likely" as in "I've liked this actor in other shows so this one should be pretty good, too," but when it comes before an action rather than a judgement it can make it sound like you are saying that person must, they are compelled to, or required to do the action. For example, "There is a test on Friday so you should read up to chapter 3 in your textbook." And in past tense (like in this example where he's already given the performance), "should" tends to be hypothetical so correcting the sentence to "he should've given a nuanced performance" is likely to be interpreted as "but he did not" even though literally it could also be interpreted as "probably did".

The はず from your Japanese version can be difficult to translate into English because while I think it maps well to "should," the nuances of "should" can be tricky and I think that's why 3/4 correctors made comments on this line.

I had no idea at all so farn't heard about it at all.

I think this is what you meant, right? That you did not know it existed?

The main character's is a chef in the drama isplayed by Kaoru Kobayashi, a very calm and cool actor.

He should be givingI expect he gave a nuanced performance.

"He gave" is good here because he was already filmed. So past tense makes more sense.

The Japanese TV Drama Titled 「深夜食堂」("Shinya shokudou"「深夜食堂」)

I was told by a Hungarian that "Shinya Shokudou（Midnight Diner）" is an interesting drama.

I had no ideat heard of it at all so far.

The main character's chef in the drama is a chef. This role was performed by Kaoru Kobayashi, a very calm and cool actor.

He should be giving a nuancedmust have given an outstanding performance.

I was told by a Hungarian (person/friend) that "Shinya Shokudou（Midnight Diner）" is interesting.

I had no idea at all so farn't heard of it before.

The main character's chef in the drama is, a chef, is (played by) Kaoru Kobayashi, a very calm and cool actor.

The"Shinya shokudou"「深夜食堂」 , A Japanese TV Drama Titled "Shinya shokudou"「深夜食堂」

I was told by a Hungarian that "Shinya Shokudou（Midnight Diner）)" is interesting.

I had no idea at all so farever heard of it.

He should be giving a nuancemust have given a good performance.

What you wrote here made no sense to me.
I translated your Japanese text to come up with this correction. :-)