If a person has wet dream and due to sickness, etc. he can't take bath but he can make ablution (Wudu)? So in such a case should he make ablution or Tayammum (even having water) for prayer? 1) Can he pray, or after finishing the problem (sickness) can he make Qadha? 2) Can he be imam?3) In this condition can he recite Qur'an, or make Istighfar, or Salat Salam,4) Can he enter to mosque?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Whoever is in the state of major impurity and cannot perform Ghusl for an Islamic sound reason, he has to perform Tayammum (dry ablution). He should not perform ablution, since ablution does not remove the major impurity. The prayers performed by dry ablution are valid, so he should not repeat them again.

He can also lead the people in an obligatory prayer as narrated from ‘Amr Ibn al-Aas who said: 'I had a wet dream on a cold night in the battle of Dhat as-Salaasil. I was afraid, that if I performed Ghusl I would die. I, therefore, performed Tayammum and led my Companions in the Fajr prayer. They mentioned that to the Prophet who said: “ ‘Amr, you led your Companions in prayer while you were sexually defiled? I informed him of the cause, which impeded me from performing Ghusl. And I said: 'I heard Allah says: “Do not kill yourselves, verily Allah is Merciful to you”. The Prophet laughed and did not say anything”. [Ahmad and Abu Daawood]

Therefore, after performing dry ablution such person may enter the mosque in order to perform the prayer or for any other purpose but he must not enter a mosque before performing Tayammum. He may also supplicate Allah and invoke blessings on the Prophet Muhammad . It is also permissible for him to recite the Quran according to the most correct opinion of the Muslim scholars.

For more benefit, please refer to Fataawa 241396, 357823, 354112, and 92216.

Allah knows best.