What about wearing a silver necklace with Ayah al-Kursi? What about mixing with girls without touching, only speaking?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Wearing a silver necklace or bracelet is not permissible for men since it is an imitation of women. The Prophet (Sallallahu Alaihi wa Sallam) prohibited such practice. However, wearing a silver ring is permissible but wearing gold is strictly prohibited for men. Only women can use gold and silver to adorn themselves.
Know that one must avoid entering into toilet or any other inappropriate place with verse of al-Kursi or Allah's Name.
A woman should also know that showing her beauty/adornment to men except her husband and Mahram (unmarriageable person) is not permissible.
As for your second question, please read the Fatawa: 81516 and 81433.
Allah knows best.