If I buy a new domain and would like to add adsense into it, do I need to inform google that now I have another domain (other than the main one) ? I think someone mentioned that once your account approved then you can add adsense on any additional domains without letting google know about new domains, is this correct ?
You don't need to inform Google. Just add it to your adsense account and you can use it. You can use your one Adsense account on all your sites. - Mr.President -
do we need to added it to our adsense account or just inserting the same previous already made google codes into the new domains ?
don't add it. ("allowed sites" is not for that) you can generate a new code for any of your sites that you want. there is no review process for any sites that you make in the future.