What is Court Marriage & how is it solmnized??

There is no court marriage and hence no procedure of solemnization. Could you explain what is "amp"

A marriage which has already been solemnised can be registered either under the Hindu Marriage Act, 1955 or under the Special Marriage Act, 1954. 

 AS PER MY INFORMATION ONE MONTH'S PRIOR NOTICE IS REQUIRED TO BE GIVEN TO THE COURT. THE COURT DISPLAYS THAT NOTICE AT ITS NOTICE BOARD AND IF NO OBJECTION AGAINST MARRIAGE IS RECEIVED BY THE COURT WITH IN THAT ONE MONTH PERIOD THEN WE CAN GO AHEAD WITH THE MARRIAGE. 

For court marriage, we need to submit proofs of age and residence for both bride and groom. 2 passport size photographs are needed of both bride and groom.

3 witnesses are required at the TIME OF MARRIAGE

Does special marriage act  works where both person marring  are of same religion?

I think 'amp' is mis printed. it doesn't any mean.

it might be HMP=Hindu Marriage Petition

Yes, your information is absolutely correct. The phrase has come to be known as Court Marriage since such marriage is performed in the Court i.e. in the Marriage Registrar's Court. Another phrase for such a marriage is Civil Marriage. In strict legal parlance there is no word like stay order but laymen do use it because a particular party is stayed from doing something- refrained from doing. whereas the correct legal term is Injunction. Similarly the phrase court marriage is used by commonners which is also easy to understand. If I am not wrong, any two consenting adult male and female can marry under the Special Marriage Act. However, it is specially designed for  marriages of special kind like between persons from different community/religion.

No court marriage under law