Is placing a towel bearing the name "Ain Ibrahim" on the ground considered an act of disbelief (kufr)? And what is the ruling on smiling when greeting with salaam?

Throwing the aforementioned towel does not constitute disbelief (kufr), and it appears the questioner is suffering from obsessive whisperings (waswasa). The scholars have stipulated that discarding anything containing the names of Allah or the names of the Prophets with the intention of mockery is an act of disbelief (kufr). Every branch of Islamic knowledge or anything bearing a revered name is treated similarly to the Qur’an in ruling, with the condition that there must be an indication of disrespect for anything other than the Qur’an. As for smiling at a Muslim, it is an act of recommendation (mustahabb).