MB 1: For Rosh Chodesh - This is the wording in many texts. In the explanations of the Gaon of Vilna, he says that the intent here is the Mussaf [Additional] prayer, because it is said only infrequently and therefore are not so familiar. The Pri Megadim draws from the Bach and the Pri Chodosh, who say that the same is true for "Yaaleh V'Yavo" [the Rosh Chodesh addition] of the standard morning prayer as well as the additions during Chanuka and Purim - all of these also need to be prepared in advance or else read from a Siddur. In the Shiurei Knesses HaGedolah, the author expresses amazement at the custom of some people to be lenient with all of this, to pray by heart without advance preparation, because he does not know upon what they rely. See also in the Shaarei Tshuva. Certainly, in the ideal it is proper to be careful to pray on Chanukah, Purim, the holidays and Rosh Chodesh, at least the first prayer (of each holiday) from a Siddur, and this is sufficient.
MB 2: Praying by heart - The Machatzis HaShekel writes that many people follow an improper custom, saying the blessing of Kiddush Levana [Sanctification of the New Moon] from memory and not preparing in advance. See also in the Shaarei Tshuva.
MB 3: From a Siddur - Certain prayers and piyutim which are difficult to understand must always be prepared in advance, and having a text does not exclude one from this requirement (Taz).