In most western countries they do not use water in their' toilets, instead they use papers. Is it permissible to use them? After using then is it permissible to perform prayers without using water?

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.

It is permissible to remove impurities with paper, tissue or small stones, since it is not a must to use water to clean private parts after answering the call of nature. But, if the impurity spreads beyond the normal area, then using water becomes necessary, and needed. Otherwise, using water will be desirable.

Thus, one can perform his/her prayer after purification by stone, tissue or paper.

Allah Knows best.