Is it possible for a Jinn to possess a human being?

Before answering this question, let us consider this verse, "And I have not created the Jinn and the men except that they should serve Me." (51:56) As both of them have been bestowed with wisdom and desires, the duty of all humans and Jinns is to serve the Almighty by controlling their desires and practicing wisdom in the Right Path.

Therefore, Jinns whose desires empower their wisdom (or intellect) are those affected by Shaitan. Those Jinns who are influenced by Shaitan are capable of harming anyone, just like those humans who are influenced by Shaitan are capable of harming anyone.

How can one stay away and be saved from possession by Jinns?

Firstly, if a human lives with Taharat (spiritual purity) and remembrance of God, then no Jinn can cause harm to him. Secondly, one can be saved from the possession of Jinns if one recites Sura Jinn (chapter 72) and Sura Naas (chapter 113) from the Holy Book, and then can do several activities like blowing these chapters on a glass of water and drinking it.

Can evil Jinns or Jinns influenced by Shaitan enter holy shrines, mosques, Islamic centers, or such places?

It is not probable that a Jinn influenced by Satan could enter an Islamic center or such places, as these places are pure and filled with the intent and action of worship. It is also very difficult for Jinn to cause harm to anyone or anything in such places.