Silja wrote: Hmmm... If I look up some verb from a dictionary (for example
Yahoo!'s), how can I know whether the verb is regular or not? Or do I just have to know it somehow...
Unfortunately, yes.

I think it will be helpful to have chances to listen with the vocabularies as many as possible.
Silja wrote:manyakumi wrote:이었다 can be shorten as 였다.
How common this is? Is it more a rule than a exeption?
Basically it depends upon the word's ending, too.
If a word ends with vowel then put 였다.
If it ends with consonant then put 이었다.
Silja wrote: Is the difference between 이/가 and 는/은 even roughly the same as the Japanese particles が/は? I mean, is 이/가 used for representing new things to listener or used in questions like "who is Jim?" or "what is happening?" (ie. when you can't identify your subject)? And then can you use 는/은 to mark the topic of the sentence, "as for", or use it in questions like "what is this?" or "where is the school?" (ie. when the subject is already known and identified)? If it's not like this, please explain a bit further. Can you use them in some sort of 는/은-이/가 pattern, where 이/가 specifies some part of 는/은? Like in sentence "코끼리는 코가 길어"?
This matter is similar to the Japanese case.
Maybe this have mentioned in other posts though,
이/가 are used for a normal subject marker or for a chosen subject among the pre-mentioned situation.
은/는 makes a word into a topic.
and sometimes 은/는 are also used for an unique condition of the subject words in order to emphasize them.
For examples,
A: 당신은 누구세요?
-> who are you?
B: 저는 존입니다.
-> I am John.
C: 존이 누구야?
-> Who is John? (among you guys)
A: 존은 여기 없습니다.
-> John is not here. (but the others are)
B: 제가 존입니다.
-> I am John. (John is me)
D: 존은/존이 누구지?
-> Who is John?
E: 존은 제 친구입니다.
-> John is my friend.
F: 누가 네 친구지?
-> Who is your friend? (among these people)
E: 존이 제 친구입니다.
-> John is my friend. (That is John)
그 사실을 네가 알고 내가 안다.
You and I both know that fact.
그 사실을 너는 몰라도 나는 안다.
You don't know that fact but I do.
Let's get into your sentence,

코끼리는 코가 길어
Elephants have long noses.
코끼리가 코는 길어
Elephant's nose is long : Long noses belong to elephants
(the word "nose" is emphasized)
코끼리 코가 길기는 하다.
This time, the word "long" is emphasized
You can even make an object word into a topic by using this marker.
There is a famous line by 송강호 from the movie 살인의 추억.
(너) 밥은 먹고 다니냐?
Well... I'm not so good at english to translate this exactly though,
It means "Can you even afford your meal?"
In this case, 밥 is an emphasized topic from an object word.
Actually the subject of that sentence would be 너(you), not 밥.
but he used a topic marker to the object 밥 so that he could make a nuance of "at least 밥", "nothing else but 밥" in the manner of sympathy.
Silja wrote: Oh, and what does this word mean: 수학. One online dictionary says that is means "education" and other that is means "math". Which one is correct?
Both are correct but
수학(數學) which means "math" is much more commonly used than 수학(修學:studying) or 수학(受學:being educated).
