Why words like 'okay' and 'taxi' are universally understood across the world but survival related ones like 'help', 'water', 'food' remained nation specific?

Populations and Languages probably already had a pre-existing word for help, water, food, before English became the trade language. When a new concept is introduced via English there is a chance the (simple) English word will be borrowed for that thing.

It's why every European language just slaps an accent mark on the word "airplane" because we invented the tech and created the name, so they just adapted it to fit the pronunciation of the phonetics in their own vocabulary.

Because you have the important words before you come into contact with another culture. You only borrow words you lack

Survival words, as you would expect, exist in every language and have existed in every language for a long long time, likely since their inception. It is rare for a word that has existed for a long time to be removed from the lexicon, especially for another languages word entirely (though it does happen).

A "taxi" as a concept is a relatively recent invention, meaning a word for it did not exist in any language before then. And by the time it was invented, the world was far more interconnected than it had once been. As such, many languages, instead of create a whole new word for this new concept, borrowed the word from the place that created it, which in this case spoke English.

A similar case exists for the word "okay". I don't know if it's just a legend or a true story, but supposedly it was a way that a former president use to give his approval on documents, stamping it with the "OK", which stood for Ol' Korral, his ranch. Regardless, "OK" (sometimes lengthened to "okay") became ubiquitous and synonymous in the US with approval or acceptance of something. Again, due to the connectiveness of the world that is only a recent development, relatively speaking, the new shorthand phrasing spread to languages where there wasn't already an equivalent. It is a handy shorthand way to express a sentiment of approval, so many we happen to adopt it wholesale.

There are similar words, phrases, and abbreviations we use in English as well, sometimes with some anglicized spelling or pronunciation, sometime just a straight carbon copy. Names of foods like "burrito" (Spanish), "beef" (French), "hors d'oeuvres" (French), "sushi" (Japanese), or "cookie" (Dutch). Concepts like schadenfreude (German), a metropolis (Greek), or avatar (Sanskrit). Phrases like "R.S.V.P." (i.e. "répondez s'il vous plaît", French), modus operandi (aka, "m.o.", Latin), Et Cetera (aka "etc.", Latin), and Faux Pas (French). The more connected the world is, the more language mixing we will have, especially as new concepts arise and are borrowed by others.

The origin of OK is unknown, but there are many many theories. My favourite one is that it's an abbreviated phonetisation of all correct - "ol korekt" based on some meme fad that people did at the time. Also apparently that was dock workers that were doing that, from which sailors caught it and they distributed it around the world.
https://www.etymonline.com/word/OK#etymonline_v_2557
Also, you reminded me of one of my favourite Wikipedia pages (see Examples section): https://en.wikipedia.org/wiki/List_of_gairaigo_and_wasei-eigo_terms

The survival related ones came to have names because they are integral to survival. People needed to address them, and so they did. With local isolation or dialects or divergence.

Okay, taxi, cola became popular and expanded their reach. They did not arise in individual and dispersed areas, they traveled.

In a similar vein, this concept is useful to try and figure out where certain technologies were invented independently and where they spread through trade.

From learning a new language, one thing I noticed is that the more modern the word, the more likely it will be the same or similar in your own language. Thus computer is very close across many languages where as help can be quite different. I think taxi would be a very new concept. For Ok. That might just be due to the word being so simple thus it was adopted fast. Much like we nod for yes.

Not an expert but just an observation I had found interesting.

Biochemistry and bioinformatics are just full of English terms. This branch of science is relatively new, and since that stuff was mostly published in English, other scientists just copied the English words and proceeded to write their articles in their own language.
That’s nothing new though. Throughout history there has been a lot of word borrowing and stealing going back and forth. If you invent a fancy new sword and you happen to be speaking Spanish, French, German or whatever, then the rest of the world will just have to deal with calling your sword by a name they can’t pronounce. Usually they’ll start using a distorted version, but the connection is still there. If you give it an easy name, then everyone might actually still use the original name. Espada ropera is too hard, so people will just call it a rapier instead. If it’s an easy word like pomel (Old French), it’s not going to change much (pommel). Taxi, and pizza are fairly easy to pronounce, so they haven’t change much while traveling around the world. OK is a different story, because writing it as okay is a very English thing. Also the pronunciation has some variation, but nothing too big.
- That is what I found interesting. Some words obviously have been around for thousands of years and likely originated on their own with little to no foreign influence. They would often have no simularities across languages. But if you did notice a word that was similar, you could almost gauge when that word originated by how far it has diverged between languages.
Nod for yes is not universal, in parts of Asia you'd wiggle your head side to side (not turn like shaking your head as a no, but actually sway your head side to side). You'd nod your head up to indicate No in Greece and Turkey among others. Bulgaria and Albania even completely swapped the yes-nod and no-shake.
But all of those places also consume North American/Western European media, so the concepts are mostly understood and even homogenising.
"Ok" was coined in the mid 1800s, new enough in the grand scheme of things
A taxi isn't a new concept. Hiring someone to drive you is probably one of the oldest concepts in civilization. All these words are used in conversations during work. If someone wants to pay you money, usually you just use whatever words they want.
If you are a taxi driver or restaurant owner, "taxi" or "cola" mean money to you. You learn quickly that way.
- oldest concepts in civilization? when the first steam powered automotive capable of human transportation was in 1769? and didn’t really gain popularity or actual usage until the 1800s?
  i mean yeah that’s near the beginning of the US and also around the time other western countries gained freedom from european slave rule (haiti, 1804; mexico 1821; DR 1844; Canada 1867, but not adopting full legal freedom until 1900s). but for the most part, most every civilization is hundreds if not thousands of years older.
  you know what’s an older concept than taxi? water. or help.

Taxi is something that travelers use a lot of. You fly into a foreign city that speaks a language you don't understand, but if the native population want to get your tourist money, they better know what you call a "car for hire" service. Seems like it is an easy word to say that could be quickly adopted by most languages for economic reasons.

Plus, cars have only been around for just 100 years, so there is no historic word for a taxi that goes back 1000 years. Every language would need to create a new word for that service, so might as well just adopt what other languages use. The same is true for a lot of technology terms. For instance, I know the word "computer" is very similar in Greek, Spanish, Italian, Russian and probably a ton of other languages.

It's easy to just use sign language for those.

Waving your arms frantically, and miming a drink or eating food are pretty universally understood.

"Why are words" is a question.

"Why words are" is an explanation.

- Yeah it's only a creeping error that's making English harder and search engines worse. Fuck me sideways for politely highlighting the difference in a thread about language.
Don't worry, it's a pet peeve of mine as well, shallow and pedantic or not.