The following three forms of 2nd person pronoun "you" are used in Hindi.

You = Aap  , we use hain with aap  = used with elders or formal acquaintances.(Respectful/formal) 

You = Tum,   we use ho with tum= Used with equals .(Informal)

You = Tu = we use hai with tu = used with children, near and dear ones. (intimate)

I believe, you should use "Aap with elders and Tum with friends and other people.

I want to know how you became so happy
"how you became so happy" this sentence does not make any sense in Hindi. We use this construction but not for feelings and emotions.. We say I want to know that why you are so happy and why you were so happy. We have two ways to say this expression. we use that (ki) to join the two sentences.  Ki is required to use in Hindi sentence.

1. Main jaanaa chaahataa hoon ki aap/tum  itani khush kyo hain/ho. (if you are addressing a female)

2. Main jaanaa chaahataa hoon ki TU  itanaa khush kyo hai.

3.. Main jaanaa chaahataa hoon ki aap/tum itane kush kyo hain/ho ( if you are addressing a male)

4.. Main jaanaa chaahataa hoon ki ve  itane khush kyo hain (if you are addressing a group of people)

 2nd way (Indirect construction)

1. Mujhe jaanaa hai ki aap/tum  itani khush kyo hain/ho. (if you are addressing a female)

2. Mujhe  jaanaa hai ki TU  itanaa khush kyo hai.

3.. Mujhe  jaanaa hai ki aap/tum itane kush kyo hain/ho ( if you are addressing a male)

4.. Mujhe jaanaa hai  ki ve  itane khush kyo hain (if you are addressing a group of person.)

 

I want to be where you live (This sentence does not make any sense in Hindi.) 

We say" I want to live there where you live"  = main vahan rahanaa chaahataa hoon jhanan aap/tum  rahte hain/ho.

I want to study what you are learning in school
mai vahi padhnaa chaahataa hoon jo tum skool me padh rahe ho.  (Here " vahi” means the same.)

I want to go when he starts to talk
mai tab jana chahunga jab vo bolna shuru karega

I want to eat what you are eating because it looks good
main vahi khana chahta hoon jo tum kha rahe ho kyonki vo acha lag raha hai.

I want to know that how you became so smart (we commonly say I want to know instead of I want to understand)
main jaanaa chahta hoon ki tum  itane chatur (Hindi)  hoshiyaar (urdu) kaise bane. 

I know that why you are here
main jaanataa hoon ki  tum yahan kyo ho.

I will find who took my money 

main pataa lagaaungaa  ki  mere paise kisane liye.  ( in this example "who"  is in singular oblique because it is followed by postposition "ne", so here it means kisane. Who = kaun (nominative caae) who = kisane (oblique case).

I will find out when you will start work tomorrow
main pataa lagaaungaa jab tum kal kaam shuru karoge.

 

I want to know how you became so happy

mai janna chahta hoon ki tumne kaisa bahut khush bane tum itne khush kaise hue (Here, I used 'itne' because you mean to say, "how you became this happy". Khush generally goes with hona, not banna. You never say, khush banna, rather say, khush hona, even if someone became happy) [I used 'itna khush' before, which was wrong. Check Rishi's comment below to see why].

I want to be where you live
mai vahaan hona chahta hoon jahaan tum rahte ho (Perfect!)

I want to study what you are learning in school
mai vo padhna chahta hoon jaunsa jo tum school mein seekh rahe ho (You use jaunsa when you have a choice between different options. Think about the question word kaunsa. It means 'which'. Similarly, jaunsa is meant to say whichever, which does not apply to your sentence. Your sentence is "I want to study whatever you are learning in school". The word for whatever is jo)

I want to go when he starts to talk
mai tab jana chahunga jab vo bolna shuru karega

I want to eat what you are eating because it looks good
main us vah khana chahta hoon jaunsa jo tum kha rahe ho kyonki vo acha lag raha hain hai (Here, you use 'vah' because it is a simple subject case. Vah always changes when you add something else to it, for example, with ko it becomes usko, with se, it becomes usse and so on.)

I want to understand how you became so smart
main samjhna chahta hoon ki tum kaisa itana hoshiyaan hoshiyaar bana bane (Perfect!)

I know why you are here
mai yeh samjhta hoon jo ki tum yahaan kyon ho (This is not a dependent sentence where one situation depends on another, so we don't use jo. It is just a simple sentence with a question in between, so we use ki with a question word)

I will find who took my money
main vo  usko dhundunga jo jisne mera mere paisa paise liya liye (This sentence can be made two ways. Maybe you wanted to say, "I will find the person who took my money" which translates to what I've corrected above. But if you wanted to say, "I will find out who took my money" then this is not a compound sentence anymore, this is a normal sentence with a question in between. Then you'd say, "Mai pata lagaaunga ki mere paise kisne liye". In Hindi, find out = pata lagaana)

I will find out when you will start work tomorrow
main us tab dhundunga pata lagaaunga jab tum kal kam shuru karega karoge

I want to know how you became so happy

mai janna chahta hoon ki tumne kaisa bahut khush bane ( why were you so happy = tum kitna khush   kyo  the )  , we  don't use  'Bane'' ( became) word with happy or sad,

I want to be where you live
mai vahaan hona chahta hoon jahaan tum rahte ho

I want to study what you are learning in school
mai vo padhna chahta hoon jo tum school mein seekh rahe ho

I want to go when he starts to talk
mai tab jana chahunga jab vo bolna shuru karega

I want to eat what you are eating because it looks good
main use khana chahta hoon jise tum kha rahe ho kyonki vo acha lag raha hain

I want to understand how you became so smart
main samjhna chahta hoon ki tum kaisa itane hoshiyaan bane

I know why you are here
mai yeh janta  hoon  ki tum  yahaan  kyo ho

I will find who took my money
main usko dhundunga jisne mera paisa liye

I will find out when you will start work tomorrow
main dekhuga ( To see/watch) jab tum kal se kam shuru karoge ,