There are two issues I need suggetions and advices:

a) I received a telephone call and e mail from a company asking me to fill a application form regarding Job offer. I need to fill four professional references other than friends and relatives. I have to furnish Name, address, e mail ID, Designation and the Relationship of the references. In the relationship column, what should i write. Some of the references are ex-colleagues. I consulted with one of my friends working as HR manager in International Bank. He adviced me not to use the word Ex-Colleague in Relationship column. Kindly advice.

b) Kindly correct this sentences

Thanks for communicating with me regarding job offer. I would like to propose that I will try to shortern the notice period and make available during first week of Sep'08.

Once again, thank you for showing interest and contacting me.

a) The term "ex-colleague" might possibly give the impression that your referees are old work buddies who might not be totally impartial. That's all I can think. If you can find a legitimate way to make them sound less like they might be your friends, and more like they had a position of seniority within the company, then you might want to do that. For example, "ex-supervisor" would be better (if true).

b) I'm slightly confused. You say you've been asked to fill in an application form regarding a job offer. An application form usually precedes the job offer. Normally you fill in the application form, then if they like the sound of you they'll ask you to interview, and then finally they might offer you the job.

But, assuming you really have been offered the job, and it's not an "application form" in the usual sense, here are some suggestions:

Thanks for communicating your communication with me regarding your job offer. I would like to propose that I will try to shortern shorten the my notice period and make myself available to start during the first week of Sep'08 September 2008.

Once again, thank you for showing your interest and for contacting me. -- But this arguably doesn't sound quite right. "Thank you for your interest" would be more appropriate if they'd contacted you, say, inviting you for interview. If they've actually offered you the job then it's a little more than "interest".
Thank you Mr.Wordy

It is true. My friend working as HR Manager advised me not to mention any name of your previous colleagues or ex-boss or ex-suppervisors. The company is contacted telephonic interview (called from overseas) and they now wants to go further steps. They have internal system to fill a application form before I proceed further. Therefore, I need to fill a application form to complete formalities. I struck when I fill relationship column, I need to fill four professional references, out of which two are ex-supervisors(boss). I cant use the word friend, ex-supervisor, relative. Then what should be the right word. Kindly advice.

Once again, thank you for correcting sentences.

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It is, in my experience, perfectly normal and acceptable to use ex-supervisors/managers (whatever you want to call them) as referees on a job application form, and to describe them as such. I have no idea why your friend thinks this is a bad idea. Perhaps there are some unusual circumstances applying in your case. All I can do is suggest that you ask your friend why he advises you against this, and what he thinks you should do instead.
I know that I listed "former coworker" on my list of references as well as "former manager."
Thank you Mr.Wordy

I have already sent an e mail to friend asking for clarification. He must have some reasons to say. I will get back to you once I receive reply from him.
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Dear Mr. Wordy and Grammar Geek

I received e mail from my friend. There is a miscommunication between us. When I was asking the reference related questions over Internet chat he said dont use word "friends". In the e mail he replied saying that dont use the word friend for Co-worker, ex-supervisor. There is a communication gap what you said and what i understood. Sorry for distrubing you all. Thanks.
Don't worry at all about distrubing us, Rajay! This ended up clearing up the confusion for you. Good luck with your job.