What is the remedy for feelings of sadness, introversion, and shyness in dealing with people after sincere repentance? And is it permissible for me to search for a wife on my own, and to speak with her with the intention of marriage only in a public place?

The questioner is advised to supplicate, for Allah has commanded it and promised to respond. As for shyness, some ways to treat it have been mentioned. There is no شرعًا (Islamically) a problem with speaking to a woman one intends to propose to and marry, provided there is no الخلوة (private seclusion) or فتنة (temptation), and that the conversation is limited to what is necessary. It is also advised to seek consultation from trustworthy individuals regarding the woman one intends to propose to, and to seek assistance from righteous brothers in searching for a righteous wife, in addition to performing Istikhara.