What is the ruling on unintentional cursing or insulting, such as saying "you are a liar" or "a swindler" without intending to mock or insult? Does this fall under backbiting? And does it necessitate an apology, even if the person addressed was unaffected? What is the ruling on apologizing to someone who was playfully pushed or poked?

Emotionally charged speech that describes a person as a liar and a swindler in their presence is forbidden. It is considered a forbidden harm, and repentance and seeking forgiveness from the wronged person are obligatory, and your assumption that he was not affected by it holds no weight. However, if the speech was unintentional and a slip of the tongue, then there is no blame for it. Hitting and poking colleagues by way of joking and playing is not permissible except with their consent and without harm. Joking between colleagues is permissible as long as it does not become excessive and exceed the limits of moderation.