1.      If you had met her yesterday, you would have seen how thin she was.

could anybody correct this sentence for me.

'you would seen' is not a valid tense at all.

What I have corrected it to is the Modal Perfect. Here, it describes a past possibility that did not happen.

2.Did you hear her laugh just now.

why can't I use laughing here You can use it.

Did you hear her laugh       = Simple Past

Did you hear gher laughing = Past Continuous

3.Fewer students have played truant since the new system was implemented.

Can I say has implemented. No.

A system does not perform the action of implementing.

Someone implements a  system.

You seem to want to use the Present Pereect tense, so you must say

Tom has implemented the system

or The system has been implemented (by Tom).

Have you learned yet the various tenses I have mentionered here? If you have, you need to study them further.

please tell me reasons of the three question in detail and give many examples to compare.  No, I don't feel like spending more time on this. Do you realize that it sounds like you are asking me to do a great deal of work for you? 

Great thanks in advance.

You're welcome.

Clive