Sheikh Yusuf Al-Qaradawi adds:
We all know that the Companions of the Prophet, peace and blessings be upon him, did not celebrate the Prophet's birthday, Hijrah or the Battle of Badr, because they witnessed such events during the lifetime of the Prophet who always remained in their hearts and minds.
Sa`d Ibn Abi Waqqaas said that they were keen on telling their children the stories of the Prophet's battles just as they were keen on teaching them the Qur'an. Therefore, they used to remind their children of what happened during the Prophet's lifetime so they did not need to hold such celebrations. However, the following generations began to forget such a glorious history and its significance. So such celebrations were held as a means of reviving great events and the values that we can learn from them.
Unfortunately, such celebrations include some innovations when they should actually be made to remind people of the Prophet's life and his call. Actually, celebrating the Prophet's birthday means celebrating the birth of Islam. Such an occasion is meant to remind people of how the Prophet lived.
Allah Almighty says: "Verily in the Messenger of Allah ye have a good example for him who looketh unto Allah and the last Day, and remembereth Allah much." (Al-Ahzab: 21)þ
By celebrating the Prophet's Hijrah, we should teach them values such as sacrifice, the sacrifice of the Companions, the sacrifice of `Ali who slept in the Prophet's place on the night of the Hijrah, the sacrifice of Asmaa' as she ascended the Mountain of Thawr. We should teach them to plan the way the Prophet planned for his Hijrah, and how to trust in Allah as the Prophet did when Abu Bakr told him: "We could be seen so easily, the Prophet replied saying: "O Abu Bakr! What do you think of two when Allah is their third?" "Have no fear, for Allah is with us." (At-Tawbah: 40)
We need all these lessons and such celebrations are a revival of these lessons and values. I think that these celebrations, if done in the proper way, will serve a great purpose, getting Muslims closer to the teachings of Islam and to the Prophet's Sunnah and life.
As for celebrating `Ashooraa', the Prophet, peace and blessings be upon him, celebrated this day by fasting only. He asked the Jews why they fasted on that day and they told him that it was the day that Allah saved Moses and the people of Israel. The Prophet replied saying: "We have more of a right to Moses than you." So he fasted on that day and ordered the people to fast on that day. He also said near the end of his life: "By Allah, if I lived longer I would fast on the 9th of Muharram." That is, that he would fast on the 9th and the 10th in order to be different from the Jews who fast on the 10th only. However, some of the Sunnis celebrate `Ashura as if it were a feast. The Shi`ah consider it a day of sadness and mourning, but all such things are innovations and are completely un-Islamic.
As for the second part of the question, the exact date of the Prophet's birth is disputed , but it is most likely to be on Monday, 9th Rabee` Al-Awwal (20th or 22nd of April, 571 AC), the same year in which the invasion of the Elephants took place against the Ka`bah. And he, peace and blessings be upon him, passed away on Monday 12, Rabee` Al-Awwal in the eleventh year of Hijrah (8 June 632 AC.)
Allah Almighty knows best.
Source : http://www.sunnah.org/ibadaat/islamonline_mawlid_fatwa.htm