Lots of different things
What is the difference between saying
예쁘다 - 예뻐요
귀엽다 - 귀여워 …
What is the difference if you conjugate it or not
In Boys over Flowers Jae Kyung says to Jandi 예쁘다 when Jan Di is wearing the maid outfit and then Jan Di says 예뻐요 to Jae Kyung when she is wearing the wedding dress

What does 잖아 mean
How do you use it?

What does 어라 mean
I heard in fantastic baby

여기 붙어라 모두 모여라
붙다 means join or stick and 모이다 means gather doesn't it?
What does it mean ?

How do you say isn't it?
Like
It is cute, isn't it?
It is pretty, isn't it?

How do you say these words in Korean
To dream
To stop
To start
To mean
To laugh
To cry
To giggle
To run
To be angry
To be sad
To be happy
To be excited
To be frustrated
To be depressed
To be bad
To bed sad
To be cool
To be bored
To be annoyed
To be funny

And what is the difference between 고 싶다 and 을/를 원하다?
Do you use 고 싶다 with verbs and 을/를 원하다 with nouns
If so would you have to add 기 to a verb to make it a noun so you can use it with 을/를 원해?
Also is 고 싶어 like an ending you add on to make it want and is 원하다 the verb that means to want?

THANKS ! You don't have to answer them all just if you could answer a bit if you can c:

Question

Lots of different things 
What is the difference between saying
예쁘다 - 예뻐요
귀엽다 - 귀여워 …
What is the difference if you conjugate it or not 
In Boys over Flowers Jae Kyung says to Jandi 예쁘다 when Jan Di is wearing the maid outfit and then Jan Di says 예뻐요 to Jae Kyung when she is wearing the wedding dress

What does 잖아 mean
How do you use it?

What does 어라 mean 
I heard in fantastic baby

여기 붙어라 모두 모여라
붙다 means join or stick and 모이다 means gather doesn't it?
What does it mean ?

How do you say isn't it?
Like
It is cute, isn't it?
It is pretty, isn't it?

How do you say these words in Korean
To dream
To stop
To start
To mean
To laugh
To cry
To giggle
To run 
To be angry
To be sad
To be happy
To be excited 
To be frustrated
To be depressed
To be bad
To bed sad
To be cool
To be bored
To be annoyed
To be funny

And what is the difference between 고 싶다 and 을/를 원하다?
Do you use 고 싶다 with verbs and 을/를 원하다 with nouns
If so would you have to add 기 to a verb to make it a noun so you can use it with 을/를 원해?
Also is 고 싶어 like an ending you add on to make it want and is 원하다 the verb that means to want?

THANKS ! You don't have to answer them all just if you could answer a bit if you can c:

Answer

꿈을 위해
 중지하려면
 시작하려면
 말은하기
 웃음
 울다하기
 낄낄 거림으로
 실행하려면
 화를 위해
 슬픔을
 행복
 흥분하기
 좌절하기
 우울한
 악당이되고
 슬픈 싫어요
 진정하게하려면
 재미하려면
 화가 되려면
 농담이
Sorry, I can not make sure the sound of them in korean. Hope you can understand.

Answer

붙다 - to stick (to), adhere (to), cling (to)       
모이다 - to gather, flock, assemble, congregate, come[get] together
~어라 - I'm pretty sure it means "Do ___!" Like for an order. 
ex. Courtesy of Naver

그것을 입어라 
Put it on.

여기 있어라 
Stay here. 
______
Add ~지요
For "right?" or "isn't it?"
날씨가 좋죠 
(In speech, 지요 is usually shortened to 죠)

Answer

예쁘다, 예뻐 > casual Korean 
예뻐요 > polite Korean 

다 is a basic verb(or sentence) ending, it's got an 'as a matter of fact' feel to it.

요 is a polite verb ending. 

You're looking at a cat and say 저 고양이 예쁘다 about it. I'd look at the cat to see if it's pretty or not. If you say 저 고양이 예뻐 instead, I might say '누가 뭐래?(which roughly means 'Who said it's not?' in a joking way. So when you say 예뻐 instead of 예쁘다, you sound a little bit more insistent or pushy. 예쁘다 feels like a fact while 예뻐 sounds like it's based on your tastes or opinions.  

잖아
How do you use it? >>> http://www.italki.com/answers/question/103333.htm

-어라/아라 makes an imperative. 
가다 to go 가! Go! 가라!
먹다 to eat 먹어! Eat! 먹어라! 

How do you say isn't it? >>> -지?
Like
It is cute, isn't it? 귀엽지?
It is pretty, isn't it? 예쁘지?

How do you say these words in Korean
To dream 꿈꾸다
To stop 멈추다, 그만두다
To start 시작하다
To mean > this isn't something you should learn it this way. 
To laugh 웃다
To cry 울다
To giggle 낄낄거리다
To run 뛰다
To be angry 화나다
To be sad 슬프다
To be happy 행복하다
To be excited 신나다
To be frustrated 답답하다
To be depressed 우울하다
To be bad 나쁘다(we would say 안 좋다(not good) more often unless we say it about someone)
To be cool ...as in 'cold'?
To be bored 심심하다, 지루하다
To be annoyed 짜증나다
To be funny 웃기다

The difference between 고 싶다 and 을/를 원하다 is that we don't say -을/를 원하다 in everyday Korean, it sounds a bit formal and as if the speaker translates the English sentence into Korean. In this case we might say '내(or 제)가 원하는 건(What I want is...)' in effort to make 원하다 sound more indirect.  

If so would you have to add 기 to a verb to make it a noun so you can use it with 을/를 원해? Technically, yes. 가길 원해? Do you want to go? ...doesn't sound natural. 

Also is 고 싶어 like an ending you add on to make it want and is 원하다 the verb that means to want? Yes.