All praise is to Allah and many blessings be upon he who was, is and will be the intercessor for his ummah. On the day of Judgement the Prophet (peace be upon him) will be the first to perform intercession, this is called Al Shafa`ah Al Kubra. This will be for the infidels aswell. On the day when all will be present in Al Mahshar, the ground will be made of copper, the sun will be very close to the heads, due to heat brains will boil, people will sweat, tongues will dry and become like thorns.

Everyone will be standing there waiting for the judgement to start. The day will be equivalent to 50`000 years and half the day will pass in waiting. People will be so desperate to leave the Al Mahshar that they`ll want the Judgement to start wether they`d have to go to heaven or hell. They`ll think hell is better than the Al Mahshar. The people will go to Adam (peace be upon) asking him to ask Allah to start the Judgement, he will send them to Nuh (peace be upon him) and he will do the same until the people come to the greatest of all creations Sayyidina Muhammed Mustafa (peace and blessings be upon him).

Now the Prophet (peace be upon him) will ask Allah to begin the judgement, this is the first Shafa`ah which is called Al Shafa`ah Al Kubra. From the above one can see this will be for the kuffar aswell. This shafa`ah is only for our Prophet (peace be upon him). After this there will be no shafa`ah for the kuffar.

The shafa`ah after this will be performed to remove sinners from hell to heaven, this is only for those who died with Imaan meaning the muslims. The Qur`aanic verses negating intercession is shafa`ah for the infidels. No one will intercede for them to be removed from hell to heaven. This can be found in the commentaries of them verses, no one has said there will be no intercession for the believers.

Will anyone other than the Prophet (peace be upon him) perform shafa`ah? The answer is indeed others will. It says in Tirmizi Shareef and in Mishkaat Shareef that Abu Sa`eed (Allah is pleased with him) narrates that the Prophet (peace be upon him) said, “Some people from my ummah will intercede for alot of groups, some will interced for a community, some will for 10 to 40 people and some will intercede for only one person untill all my ummah enters heaven”. In Ibn Al Majah and in Mishkaat Shareef it say that Uthman Al Gani (Allah is pleased with him) said that the Prophet (peace be upon him) said, “On the day of judgement three types of people will intercede. First the Prophets of Allah, then the scholars of Islaam and then the martyrs”.

Commenting on the above Hadith Hazrat Abd Al Haq, Muhaddith-e-Dehelvi (may Allah be pleased with him) writes in Ashi`ah Al Lam`aat “The Prophet (peace be upon him) has specified only these three because of there high statuses, otherwise intercession has been proven for all pious people such as a haafiz of the Qur`aan who acts upon the shari`ah and a haaji who speaks the truth”.

I`m sure i need not say more. This is from what i know and as you`ve said in the question Allah knows best.
[Answer provided by: Maulana Zahid Husain]