I think that のは is essential in this sentence.
The novelty and the excellence of the noodles are the topic of the sentence, the rest of the sentence describes in what they consist.
A more simple example:
この本が面白いのは、話です。
What makes this book interesting is the story.
EDIT: I added the example (and the sumo wrestler to support my fight)
The て-form of 新しくて is used to express that the noodles are new AND superior, as in https://bunpro.jp/grammar_points/771
This makes a lot of sense, thanks! So the list is reasons why the cup noodles are new and excellent. 
I think カップヌードルが is not directly connected to でした but it’s the subject for 新しくて優れていた.
一個カップが on the other hand seems to be directly connected to でした.
I’m not sure if I understood you correctly but only the は itself is the topic marker, not the whole clause. That would be the topic.
„one cup serves three roles“ is not a noun but rather a whole clause with a subject, object and predicate. 
Here’s my take on this:
The top level structure of the whole sentence is:
X は Y でした。
where X = カップヌードルが、新しくて優れていた
and Y = 一個のカップが、三つの役割を果たす
and the の after X and the こと after Y are nominalizers
to make the X and Y clauses into nouns.
That is,
｛cup-noodle-was-new-and-excelling｝のは (topic)
｛one cup fulfills three roles｝ことでした。
or as @2000kanji translated it:
I like the grammar examples for のは on bunpro.jp (they remind me Friends episode titles) so I wrote my translation like one of them…
The thing that serves three roles in one cup was the new and improved Cup Noodles.
Nice and awkward, problem solved.
この上なく便利なカップヌードルは、一九七一年に発売されると、たちまち世界中に広まっていきました。
When these extremely convenient Cup Noodles were released in 1971, they at once spread around the world.
二〇〇七年、安藤百福は、九十六歳で亡くなりました。
Momofuku Ando died at the age of 96 in 2007.
その時、アメリカの『ニューヨーク・タイムズ』という新聞は、こんな記事を書きました。
On that occasion, the American newspaper “New York Times” wrote the following article:
この上なく便利なカップヌードルは、一九七一年に発売されると、たちまち世界中に広まっていきました。
When the extremely convenient cup noodles were released in 1971, they immediately spread worldwide.
二〇〇七年、安藤百福は、九十六歳でなくなりました。
Momofuku Ando died in 2007 at 96 years old.
そのとこ、アメリカの『ニューヨーク•タイムズ』という新聞は、こんな記事を書きました。
At that time, the American newspaper The New York Times wrote this article.
The suddenness of that second sentence caught me off guard lol
Haha, yes, they always start very slow and the describe the childhood in great detail … and then comes death. 
この上なく便利なカップヌードルは、一九七一年に発売されると、たちまち世界中に広まっていきました。
This super convenient Cup Noodles went on sale in 1971, immediately spreading aropund the world.
二〇〇七年、安藤百福は、九十六歳で亡くなりました。
Mamofuku Ando died in 2007, he was 96-year old.
その時、アメリカの「ニューヨーク・タイムズ」と言う新聞は、こんな記事を書きました。
At that time, American newspaper called New York Times printed the following article.
Easy page. I’m happy that I can read some sentences on this page and in this chapter without tools.
《ミスター・ヌードルに感謝。
«Thank you, Mr. Noodles.
インスタントラーメンは、お湯さえあれば、誰でもかみのめぐみを受けられる。
With instant ramen, anyone can receive divine grace, as long as there is hot water.
安藤は、人類の進歩の歴史に、永遠にその名を残すだろう。》
Ando will forever be remembered in the history of human progress.»
安藤百福（一九一〇〜二〇〇七年）
Momofuku Ando (1910-2007)
夢は宇宙へ
The dream to go into space
カップヌードルを作り出した後も、安藤百福のラーメンに掛ける夢は広がりました。
Even after the invention of Cup Noodles, Momofuku Ando’s ramen dreams spread out.
二〇〇一年には、宇宙で食べられるラーメンの研究を始めました。
In 2001, he began research on ramen that could be eaten in space.
そして、二〇〇五年、宇宙飛行士の野口聡一さんが乗ったスペースシャトルに、世界初の宇宙食ラーメン、『スペース・ラム』が積み込まれました。
Then, in 2005, the astronaut Soichi Noguchi brought on board of the Space Shuttle the world-first space food ramen “Space Ram”.
「ミスター・ヌードルに感謝。
“Mr. Noodles, thank you!
インスタントラーメンは、お湯さえあれば、神の恵みをうけられる。
Instant ramen: as long as you have hot water, you can receive blessings of the gods.
安藤は、人類の進歩の歴史に、永遠にその名をのこすだろう。」
Ando - this name will stay forever in the history of human progress.”
Here is a google doodle: Momofuku Ando’s 105th Birthday
I think this chapter writing was easier than the previous one.
EDIT:
Question - how do we read these 〇 in years, for example 二〇〇五年? (not まる I suppose).
《ミスタ•ヌードルに感謝。
“Thanks to Mr. Noodles.
インスタントラーメンはお湯さえあれば、だれでも神の恵みを受けられる。
As for instant ramen, if one only has hot water, anyone can receive divine blessings.
安藤は、人類の進歩の歴史に、永遠にその名を残すだろう。》
As for Ando, in the history of human progress that name will likely be bequeathed to eternity.”
安藤百福（一九一〇〜二〇〇七年）
Momofuku Ando (1910-2007)
夢は宇宙へ
Dreams towards space
カップヌードルを作り出したあとも、安藤百福のラーメンにかける夢は、広がりました。
Even after suddenly creating cup noodles, Momofuku’s dreams relating to ramen extended out.
二〇〇一年には、宇宙で食べられるラーメンの研究を始めました。
In 2001, he started research on ramen that could be eaten in space.
そして、二〇〇五年、宇宙飛行士の野口聡一さんが乗ったスペースシャトルに、世界初の宇宙食ラーメン、『スペース•ラム』が積み込まれました。
Then, in 2005, on the space shuttle pilot Souichi Noguchi rode on, the world’s first space food ramen, Space Ram, was loaded aboard.
I think this might be the NYT piece that this chapter borrowed quotes from: Opinion | Mr. Noodle - The New York Times
Yeah, a few tricky sentences aside, there weren’t very many new grammar points in this chapter. Made it an easier read! I enjoyed it for that.
I think they would just be read as ゼロ. れい also means zero, but I see ゼロ more often.
Wow so poetic:
Ramen noodles have earned Mr. Ando an eternal place in the pantheon of human progress. Teach a man to fish, and you feed him for a lifetime. Give him ramen noodles, and you don’t have to teach him anything.
Google says にれいれいごねん,
ichi.moe says にせんごねん.
I would prefer the latter (only my personal preference).
I am also (slightly) better at reading the katakana ヌ (although I still misread it as タ on the last page…)
The plastic-and-foam part is a bit weird though…?
I assume it’s the foam container with plastic utensils? I can find examples of foam noodle cups and plastic noodle cups but not really any that would be a mix of the two…
If anyone hasn’t watched Tampopo before, I’d recommend it BTW. It’s a love letter to ramen specifically (not sure how the characters in the film feel about カップヌードル) and it’s pretty funny.
