A simple character but also very,very frequent one so we will dive in  to 在 today.

Character: 在

Traditional form: 在  

Pinyin: zài

Meaning:  at , in , on , up to , to rest with , to consist in , to depend on , to be alive , living , to be present , to exist , used to indicate a progressive tense

Frequency: 7

Strokes: 6

Decomposition:

 + 丨  + 土   土 (earth) suggests the meaning while  provides the sound.

Radical part: 土 ,tǔ

Radical meaning: earth, soil

Stroke animation: (the strokes are drawn the direction the picture is tipping)

Etymology: This is a pictophonetic character

The sound is taken from 才 (cái, talent, ability; just, only)  and the meaning from 土 (tǔ, earth). The earth does exist even though the debate if it is round or flat might have been under debate ( sorry, that where a bad joke). The original meaning was " to exist, to live". Man do live,exist on earth. It where eventualy extended to also mean "be loacted in" and like.

Link to nciku usage of the character 在 :

http://www.nciku.com/search/zh/detail/%E5%9C%A8/1318957

Example words:

指南 zhǐ nán to guide 
南京 Nán jīng Nanjing prefecture level city on the Changjiang, 
南海 Nán Hǎi South China Sea 
南非 Nán Fēi South Africa 
南瓜 nán guā pumpkin 
南极 nán jí south pole 
南下 nán xià southward 

This is two questions, but I feel they're a bit related.

1: What is the difference between "她在看电视" and "她看着电视"? I've learned that both those contructions would mean "-ing", so is there any difference between using '在' and '着'?

2: Same question, but with '再' and '又'. What's the difference between "她再看电视" and "她又看电视"?

The reason I feel the two questions are related is because you can't actually hear the difference between the first sentences in eaxh question. Do you simply avoid confusion by using '着' and '又' instead of '在' and '再' in cases where context is ambiguous? And when you need to say "She's watching TV again", I'm guessing you wouldn't say "她再在看电视", but rather "她又在看电视" or "她再看着电视", or even "她又看着电视".

I'm sure I've misunderstood the usage of some of these characters. Please do point that out. And any pointers on the usage of any of these four characters in their "-ing" and "again" functions would be appreciated.