Usually, there are 2 kinds of pronunciation of 了. The first one is "le". We usually use this kind of 了as a auxiliary word to express a finished situation, like 我完成了 （I have finished）， or to express a tone, like 明天又是星期一了， The second one is "liǎo". Usually, this kind of 了is an verb which means “understand”, like 了解（understand），一目了然（be clear at a glance), or means "end", like 终了，了局。 Then I searched the dictionary and found that 了 still can be adj. which means "wise", like 了慧， or "clear", "light". At such situation, 了 still is pronounced as "liǎo". But I have to say, these meanings often can be found in in classical Chinese, and in usual life, we don't really use 了in these ways. Or it can be used as adv. with "无"，“不” . When it is in front of verb or adj., it means "entirely (not)" , like 了无恐色（with no fear）. But when it is after a verb with "得", it means a possibility, like 办得了（can do it）, 你来得了来不了？（Can you come or not?） I have to say that 了is very complicated in Chinese, so I suggest you put more attention in 了 and practice more. I'm glad to answer your question.

It is used to show that you have done something or used after a sentence in which you show you are upset or sad about something,for example, when you feel tired ,you can say"我太累了".it is monday again,and i really don't want to go to school.又到星期一了，我真不想去上学。

it mean already finished something. we put it in the end of sentence normally. eg. 我吃過了 我去過了 我看過了

了 is already finished.