What is Irfan? And is it permissible in Islam to practice it, I also believe that Sufi's practice Irfan?

It is not right to depend on other than the holy Quran and the authentic narrations of the Prophet and the Ahlulbyte (peace be upon them) in the religion’s matters including Irfan. There are lots of such narrations that explain the recommended worship acts and the kind of relation a man should have with the almighty Allah. Muslims are encouraged to gain the religious and godly knowledge from these original sources only.

After doing Tayammum instead of ghusl, can I perform wudu for prayers?

Yes, if you performed the tayammum instead of Janaba ghusul and a minor occurrence happened to you like sleeping or urinating, you should perform tayammum instead of wudu before your prayer becomes valid.

As Imam Mahdi (A. S.) was hidden by God’s wish at the age of 5, what will be his age at when he reappears again?

It was narrated from the texts of the imams of the Ahlulbait (peace be upon them) that when he reappear again he would look like forty years old. Nobody knows saves Almighty Allah his original age after the reappearance.