Is it permissible too wear fake nails and nailpolish? I heard many times that it's not batil by Sayed Muhammed Fadlallah but I can't find it.

Fake nails are allowed if they are easily removable for ablution and ghusl, otherwise, they are not permissible.
Also they are not permissible if they are going to be seen by foreign men.
Nail polish is allowed according to S. Fadhlulla.