I know that the word "to" ... I would appreciate your help.
Both are correct and mean the same. Although the first one isn't much used in practice.
Your example "TO jest prezentEM dla kolegi."
Theoreticaly yes... If you treat "to" as a replacement for "ono". But "to" is so special that it doesn't behave like this.
"To jest prezent dla kolegi" - this is a present for my/your co-worker/co-student/friend (not a very close one)
It's how I would say this.
"Mówić TO srebro, milczyć TO złoto." = Silence is golden.
"milczeć", apart from that it's correct, but actually we say:
"Mowa jest srebrem, a milczenie złotem"
This is a proverb, so it's fixed and you shouldn't change it to other theoretically grammatically correct versions.
Other times, "TO" can mean "it", e.g. "TO jest ważne być czujny." = IT's important to be vigilant. etc..
"To jest ważne, żeby być czujnym" (if you want to emphasise that "THIS is important" and not anything else), even better extending it to:
"Właśnie to jest ważne, żeby być czujnym" (which makes more sense - "exactly THIS is important, to be vigilant" - I think, in English you would have to put a comma here)
"Ważnym jest, żeby być czujnym"
"Ważne, żeby być czujnym"
The last one is most commonly used. Although it's not even considered a sentence in Polish grammar, it's a so called "sentence equivalent" because it has no predicate (main verb, as "jest" in both two).
Why "czujnym" in all the sentences and "ważnym" in the second one? I am not sure if this is the exact rule, I am not a linguist and noone teaches such things at school - but from what I understand:
1) normally when you put an adjective without a noun after "to be", it appears in nominative (in a gender equivalent to the subject it describes - "to" is neuter, so we have ważne
) - this is something which you definitely know learning Polish, even if you started only a few lessons ago, hence you say: "jestem czujny", "jest czujna"
2) when you put there a noun described by an adjective, it appears in instrumental: "jestem czujnym człowiekiem", "jest czujną kobietą"
3) the weird thing: when we have a "subjectless" construction, not such one where the subject is default ("jestem czujny" = "ja jestem czujny", "jest czujna" = "ona jest czujna"), but such one where you cannot determine a subject (for example if "to be" is used in infinitive - but not only), this adjective, connected to the "to be" verb, not only appears in masculine (which is the "default" form of any adjective), but, last but not least, it appears not in nominative, but in instrumental, as if there was actually a noun which this adjective described!
So in "Jest ważnym, żeby być czujnym" (you can exchange the order), "być czujnym" is, of course, an infinitive phrase, but also "jest ważnym" is a "there is"-ish phrase. In English you say "It is important" because you basically don't use "There is" for adjectives, only for nouns, but this "it" plays here exactly the same role as "there" in "there is". It doesn't mean anything, it's just a "dummy subject" as you said. The thing is, in Polish you don't need a dummy subject and "to" doesn't actually play this role. It does mean "this". That's why I did put a comma in the English translation of a sentence somewhere above.
Why "to" is translated to English not only as "this", but also as "ono"? Because "it" can mean the same as "this".
"This is a book"
"It is a book"
Is there any meaning difference between these two sentences? I am not an expert, but I have a feeling these are just two ways of saying exactly the same. Although for some reason on lower levels of my education in English usually the version with "it" was only used, while when I was doing my CAE and CPE, it was often required to use "this", especially when a new sentence reffered to the previous one...
Yet the last one...
"Ważne, żeby być czujnym"
You replace the main clause with a single adjective, and then it appears in nominative neuter singular. Why so? Don't ask me. Probably because you can extend it to:
"To jest ważne, żeby być czujnym"
You will ask: "Cannot I extend it to: <<Jest ważnym, żeby być czujnym.>>"?
Yes, you can.
You will ask: "Cannot I extend <<Jest ważnym, żeby być czujnym.>> to: <<To jest ważne, żeby być czujnym.>>"? If I can, why does "ważne" change to "ważnym"?
I am afraid you must just accept it without asking. Or ask the linguists, maybe they will find an explanation for that.
Sometimes in Polish, distinctions between "this" and "that" are not as straightforward as in English
Basically "this" = "ten"/"ta"/"to" (depending on the gender), "that" = "tamten"/"tamta"/"tamto", the difference depends on the distance. The difference is that both languages set the border between "close" and "far" at different points.
This is an example from a videoblog for Poles learning English: youtu.be/1Jtt6cjrFrE?t=183
In English: "this is Chandler" but "that's Phoebe". In Polish "to jest Chandler" and also "to jest Phoebe". The distance difference is enough to distinguish between "this" and "that" in English, but not in Polish.
You just don't use "tamto" instead of "to" as frequently as "that" instead of "this".
I don't think it has anything in common with the existance of the articles.