Please explain through Quran.
see my answer https://islam.stackexchange.com/a/32792 . and i have explained it through quran.
I have heard that in Islam three divorce are given with the interval of a month.
you can see from my answer 32792 that this is not correct. you say about divorce that should be counted, when it is counted till 3. 1 month is interval invented by some scholars to solve triple talaq problem, but that is incorrect solution. divorce is counted after iddah is fullfilled.
And of divorce in iddah if they change their mind they can get together.
this is true, and husband can easily take his wife back within iddah (waiting term of 3 periods...).
And girl get notice through court how does she know that she get three divorce or not?
quran does not set court as requirement, but, as you can see in quran 65:2, after iddah is fullfilled, 2 witnesses should witness that divorce is accomplished and one more divorce is counted. as soon as you are fully divorced (fully means with iddah passed) 3 times without you marrying other men after that divorces, (and this means that you are like remarried same man 2 times, after 1st and after 2nd divorce), you cannot remarry same man, before you marry other man and divorce. and for example, if anybody lies that you are not yet divorced 3 times, you can go to court with your witnesses of the 3 divorces and proof that you are divorced 3 times.
If Islam give us right to give divorce in interval of a month then how is possible through court?
as i said, islam does not give right to divorce after 1 month, but after iddah, and court can defend you even after 1 divorce (with iddah and 2 witnesses), if your ex-husband tries to to lie saying that iddah has not passed and take you back without your agreement. but you should have reliable, trustworthy witnesses. maybe in some countries divorce is witnessed and also additionally written in documents of special governmental divorce registration bureau, and maybe that document also can help you in court.