Many people report some statements which they attribute to the Prophet, sallallaahu alayhi wa sallam, like, "Paradise is under the feet of the mothers.”, and “Whoever learns a language of a people, he is more aware and secure from their evils or plots.” What is the authenticity of these statements? Are they really narrations of the Prophet, sallallaahu alayhi wa sallam, or just statements of some people?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

This expression "Paradise is under the feet of the mothers.”,  is not confirmed to be said by the Prophet however, its meaning is correct and is confirmed in another narration in which a man came to the Prophet asking him permission to fight with him in Jihaad and he had a mother, so he told him: "Stay with her as Paradise is under her feet.” [Ahmad, An-Nasaa'ee and Ibn Maajah]

As regards the expression “Whoever learns a language of a people, he is more aware and secure from their evils or plots.”, is not confirmed to be a narration of the Prophet as far as we know after investigation, but its meaning is correct. 

Allaah Knows best.