I was wondering about if its ok to supplicate during Sajdah, and if its ok to supplicate silently when I'm out and about?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. Making Du'a during prostration is permissible, yet it is likeable. So, multiplying supplications during the prostration is recommended. The Prophet (Sallallahu Alaihi wa Sallam) said: The servant is nearest to his Lord when he is prostrating to Him. So, multiply making supplications in this state . [ Ahmad Muslim and Abu Dawood ] It is likeable to strive hard in making Du'a during the prostration since the Prophet (Sallallahu Alaihi wa Sallam) said: I have been prohibited from reciting while bowing or prostrating. During the bowing glorify the Lord. During the prostration, strive your hardest in making supplications. Most likely, you will be listened to it . [ Ahmad and Muslim ] As for making Du'a silently during your daily activities it is permissible provided your heart is attentive so that it realizes what is being uttered. On the other hand, it is desirable to make Du'a neither quietly nor loudly; rather it should be in an intermediate sound so that one can hear his own words. Allah Says (interpretation of meaning): {And remember your Lord by your tongue and within yourself, humbly and with fear without loudness in words in the mornings, and in the afternoons and be not of those who are neglectful.}[7:205]. In the same Surah Allah also Says (interpretation of meaning): {Invoke your Lord with humility and in secret. He likes not the aggressors. }[7:55]. The Prophet (Sallallahu Alaihi wa Sallam) used to make Zikr (remembrance of Allah) in all times; supplications are also a form of Zikr. However, the more a person is entirely engaged in Du'a; observing the good and recommended etiquettes of Du'a such as being in the state of Taharah, facing to the Qiblah, and raising hands, the more his supplications would be responded to. No doubt, such supplications are more worthy to be responded to than those which are made while a person is busy in his mundane matters.     Allah knows best.