Valda, I am glad if my explanations are useful

In the first place, please notice I've just corrected a typo. I typed "предстваление" instead of "представление" by mistake.

Now I'll try to answer your questions.

Quote Originally Posted by Valda View Post
"Much of it - thanks to the people of ... "
I thought that whenever the word "of" appear in the sentence you use genitive. Is it not the case when refering to people?
It IS genitive. But check this example: "Многое из этого - благодаря людям из MASTERRUSSIAN.COM." What do you expect to be in genitive? "MASTERRUSSIAN.COM"? Technically, I can say it is in genitive. But there is no way to decline a WWW site name like that.
What I have corrected in your sentence is the preposition you chose. I replaced "от" (which would not work) with "из". But both of them (either "от" or "из") do require genitive.

Let's consider another example: "Многое из этого - благодаря людям из России." Now "Россия" is in genitive. Does it make sense now?

And notice: in English you thought of using "of" (thanks to the people of ...). In Russian it is more like "from" in this specific case.

Quote Originally Posted by Valda View Post
But you have a noun after a verb--shouldn't it be "accusative"? Unless достичь is one of those special verbs.
Not always! It depends on a verb. I have already posted an explanation about "verb government" in this forum: Sentence in accusative or dative case? (please see Post #6 there).
So, yes, you just have to memorize "достичь чего?", not "достичь что?".

Quote Originally Posted by Valda View Post
But it's more like "рекомендую ДЛЯ..." figured after "для" always comes genitive.
In Russian, there are two options with "рекомендовать": either "рекомендую для студентов" (recommend for students) or "рекомендую студентам" (recommend to students). I would prefer the second option. But the first one is also possible.

And another piece of advice for you: You are trying to identify Russian cases based on the prepositions used in English. That will not always work. There is no "1 to 1" correspondance between prepositions used in different languages. A more effective way would be to learn how specific Russian words are used in specific structures.

If you "recommend doing something", there is only one option: "рекомендовать кому?". E.g. Я рекомендую тебе прочитать эту книгу.
If you "recommend a thing", there can be two options: "Я рекомендую этот сайт студентам, ..." or "Я рекомендую этот сайт для студентов, ...". But the second option is more specific, it does not always work. For example, I would not say: "Я рекомендую для тебя эту книгу", I would stick to "Я рекомендую тебе эту книгу".

So, for the beginning, just remember: "рекомендовать кому?".

... I was thinking over the difference between "рекомендовать кому?" and "рекомендовать для кого?"

The option with dative ("рекомедовать кому?") is more like giving some personal advice. You can even replace "рекомендовать" by "советовать" (to advise): "Я рекомендую тебе эту книгу" = "Я советую тебе эту книгу". "Я не рекомендую тебе туда ходить" = "Я не советую тебе туда ходить".

The option with "для" + genitive ("рекомендовать для кого?") is more like promoting something to a specific group of consumers.
"Я рекомендую эту книгу для людей со слабым зрением" (I recommend this book for the people with bad sight), i.e. I declare this book is good for the specific group of people.

Therefore, in your specific example the both options would work.

Quote Originally Posted by Valda View Post
How come? What's the "и" gotta do with anything?
Но у меня есть и другие причины: Hmm, first I just felt like inserting "и" here as it would sound better with it. But after you asked me "why", I started thinking... And that's what I have found out:

If you do not use "и" (Но у меня есть другие причины), it is more like "But I have other reasons", or "But I have different reasons". In some contexts it could be understood as "not those reasons, which I mentioned before, but other reasons".
Inserting "и" adds the meaning of "in addition to". You mentioned some reasons before and then you add: "Но у меня есть и другие причины" (But I have other reasons as well). Now it is clear that you are going to add something to what was mentioned before.

There's another example to explain it:
(A) - Я учу русский язык.
(B) - А я учу другие языки.
It means:
(A) - I learn Russian.
(B) - But I learn other languages.
Person "B" does not learn Russian, (s)he learns other languages.

(C) - Я учу русский язык.
(D) - А я учу и другие языки.
It means:
(C) - I learn Russian.
(D) - But I learn other languages as well.
Person "D" learns several languages, including Russian.

Quote Originally Posted by Valda View Post
Well, in English you can say "I invest many hours a day studying X"... and it works. Is it different in Russian?
The verb "инвестировать" is a loan word in Russian (came from English). Loan words usually have much narrower usage than they do in the language of their origin. That's not only for this specific word, and not only for Russian, BTW

"Инвестировать" is quite a new word in our language. If am not sure, but I think it appeared in 1990-s when the market economy started developing. It is mainly used in very special contexts, and sounds too bookish. For example, "Иностранные компании инвестируют капитал в российскую экономику" (Foreign companies invest their capital to the Russian economy). I even think that some less educated people do not understand what it means (again, I am not sure). Nevertheless, it is very professional, very specific and very official word.

Quote Originally Posted by Valda View Post
What exactly makes this sentence instrurmental? The "чувствовать"? If anything, I would imagine it's accusative since it an adjective that comes after a verb.
Yes, the verb "чувствовать себя" requires instrumental in the examples as follows:

Я чувствую себя героем. - I feel like a hero.
Я чувствую себя космонавтом. - I feel like an astronaut.
Я чувствую себя больным. - I feel ill.
Я чувствую себя обиженным. - I feel hurt.
etc.

Literally, this expression is something like "I feel myself to be...". The verb "to be" (быть) requires the instrumental: "быть героем", "быть больным" etc. The same is true for "чувствовать себя".

BTW, it is a very typical mistake Russians often do when speaking English. They use "I feel myself" expression. For example, if you are unwell, we usually say: "Я плохо себя чувствую". Russian people tend to translate it literally into English: "I feel myself badly"