Could you please correct me

01. Logo design for "Georgian American football federation" ( Do I need the article after for? ) Yes, "the". In this case because there is only one Georgian American football federation, or at least there is only one that you're referring to here. BTW, if the official name is "Georgian American Football Federation," in English you need to capitalize all of the words in the official name.

02. I want to add one thing, when you open the letterhead it will appear a bit faded but no worries[you need punctuation here--you can use ; or --] after printing it will be normalized [maybe instead "it will appear normal" is better, because "to normalize" is a specific verb and I don't think it's what you mean here] and if you want to get letterhead without white edges [or "borders", but you can also call these "edges"] after printing ( as shown in <s>on</s> <s>the </s>image 01 ) then you should convert "word "file into "PDF "and<s> only after</s> then it will be printed normally ( as shown in <s>on the </s>image 02 ) ( can you please check and tell me what kind of mistakes I made )

Thanks in <s>A</s>advance 🙌

Is it more important to work quickly and risk making mistakes than to work slowly and <s>make </s>do it right? ["Make (something) right" means, for example, that you've offended someone and you want to "make it right" by apologizing. Meaning, you've caused some kind of problem, and you need to fix it.]

With the accelerating [development of social productivity] [the meaning of this isn't clear to me], there are an increasing number of people who work quickly and take risks frequently, whereas there are still some people who tend to [keep a slow-paced life][this isn't quite right. You could say "lead a slow-paced life" (if they generally approach life in a slower manner) or (better, in this context) "work at a slower pace"] and try to [make everything correct][you can definitely say this, but I would say "do everything correctly/perfectly/right". Also, remember that you need an adverb here ("correctly"), not an adjective ("correct")]. From my point of view, I believe that <s>risking frequently</s> [you can't say this because the verb "to risk" requires an object (you can only "risk (something)". Instead, you can say "taking frequent risks" or "taking risks frequently"] and working quickly is more crucial in modern society.

Firstly, it meets the needs of our ever-changing environment. Take programmers in Internet companies [I don't quite know what you mean by "Internet companies". Maybe you mean companies that operate online or simply "tech(nology) companies"?] for [an] [I would say "Take (this), for example" or "Take (this) as an/one example"] example. Nowadays, the demands of customers and markets change so rapidly that there will be a lot of features to be added to a software product, for example, What's app. Otherwise, it may be at a disadvantage in the battle with its rivals, for example, Skype. In this case, as the saying goes, "Done is better than perfect.". [You don't need two periods. For British English, put the period after the quote. For American English, put the period inside the quote.] Programmers must react and program quickly to implement the required functions, although there may be some small bugs in their products.

In addition, working quickly gives us <s>a </s>timely positive feedback ["Feedback" is a collective noun (always plural, like "rice"). But you can say "a piece of feedback" if you specifically mean just one]. Because finishing a task in a short period of time affords us a sense of achievement. We can gain loads of skills quickly, become more confident, and have more time left to do something we really like, all of which serve as <s>the </s>a wonderful catalyst that motivates us to work harder and progress faster. Therefore working quickly can be conducive to our [self- ("self" is optional here but might be clearer)]improvement.

Admittedly, working too quickly can lead to quite a few mistakes. Hence, working slowly seems to be a good option. However, there may be some problems in making sure every detail is perfect. Firstly, this process can be really time-consuming and tedious, which can be a psychological challenge for some people. Moreover, working slowly can bring about procrastination, which is not beneficial for our work.

To sum up, as far as I am concerned, working quickly and risking making mistakes [is of significance][I know what you mean, but we wouldn't use that phrase here. I think you could simply say that is "is important", which sounds more natural here.]. Because not <s>just </s>only [the phrase is "not only....but"] does it satisfy the requirements of a modern society that changes rapidly, but <s>also</s> it also makes contributions to our personal improvement.

The c<s>C</s>orona generation

When we look back on history, [we see that/it's clear that/etc.] every generation experienced social events <s>which </s>that changed their <s>life </s>lives. For baby boomers (now 56~74 [we don't use ~ ... you should use a dash (-) for date ranges] years old), they are it was [1. "They" is confusing here because you've just been talking about the baby boomers. I would say "It"--it being understood that I'm referring to an example of one such "social event". 2. I would use the past tense because the events occured in the past.] the <s>Vietnamese war </s>Vietnam War and the civil rights movement. For <s>X generations</s> Generation X [or "Gen X"] (40~55 years old), it <s>is </s>was the AIDS <s>disaster</s> crisis/epidemic [we normally don't say "disaster" in the context of a health crisis]. For millennials (24~39 years old), the 2008 financial crisis had a big impact on their careers. <s>The big </s>Major [1. Omit "the" here, because we are talking about social changes generally. 2. "Big" sounds a bit too simple in this context.] social shifts [or "changes" (sounds better to me)] such as the policy of apartheid are likely to cause generation gaps between the younger <s>youth </s>and the <s>upper </s>older generations. Why does this happen? Because experiencing big [again, "major"/"significant" etc] events <s>while they mold their character</s> during a pivotal period of one's life [you can't really mold your own character--an event or other external factor molds your character. So here you can't use this construction. Instead you could say something like what I've written, which I think is what you mean] <s>effects </s>has an impact on <s>their </s>one's identity and sense of values. And for <s>Z generations</s> Generation Z (5~23 years old), the pandemic of Covid-19 will be a memory that <s>e</s>affects <s>on</s> their<s> life</s>lives [or I would just say "affects them", but that's a stylistic choice] in some form throughout their <s>life </s>lives. They are called the “corona generation” on <s>twitter </s>Twitter. Nobody knows <s>how </s>what their sense of values will be like ["like" is optional here; I would not use it myself].