[1] Conversations among the judge and lawyers (as opposed to testimony under oath) are colloquies.
The term may be applied to the conversation that takes place when a defendant enters into a plea bargain and the judge is supposed to verify that the defendant understands that he is waiving his right to a jury trial.
[3] The defendant needs to understand the charges against him, the penalties that he will face, and his rights before entering into a guilty plea.
In the US, that includes describing the rights guaranteed by the Fifth and Sixth Amendments as well as a caution that non-citizens who are convicted of crimes risk expulsion from the country.
A defendant who denies guilt may still "plead down"—plead to a lesser offense than the accusation—provided the Court allows it and provided the accused intelligently concludes on an open record that a plea is in her/his best interest (such as avoiding incarceration or a more serious charge/conviction).