Is it permissible to perform tayammum for Fajr prayer for someone who finds great difficulty in leaving his room to perform wudu at night, knowing that he has no other place of residence and that the landlord does not pray?

Tayammum is not permissible except when water is unavailable or cannot be used due to illness or similar reasons. As long as the questioner is not prevented from performing ablution by an illness, but rather by embarrassment from the homeowner, then tayammum is not permissible for him. Instead, he must perform ablution, even with the presence of embarrassment, unless doing so would lead to harm to himself or his property. He must also advise his brother to stop abandoning prayer and explain the importance of prayer and the punishment for abandoning it.