Seeking clarification on the Tiruvaradhanam kramam (method/order) on days of masa pravesha and Amavasyai tharpanam-s. Is it – morning Sandhyavandanam, Tiruvaradhanam, madhyahnikam followed by tharpanam, or is it morning Sandhyavandanam, Tiruvaradhanam, tharpanam and madhyahnikam? (How early can madhyahnikam be performed?)

Generally, Amavasyai tharpanam, etc. are to be performed after madhyahnika kalam at kutapa kalam (when the sun is hot) or aparAhna kalam (afternoon). Hence, Amavasyai tharpanam is done after morning Sandhyavandanam, madhyahnikam, and Tiruvaradhanam.
Sometimes, when it is not possible to wait until such a period, the office goers do this early in the order mentioned.
Regarding masa pravesha tharpanam, at times the advent of the month is early in the morning. During such occasions, one can after performing morning Sandhyavandanam, one can do masa pravesha tharpanam, followed by madhyahnikam and Tiruvaradhanam. If the advent of the month is in the afternoon, one can follow the order prescribed for Amavasyai.
Madhyahnikam is meant to be performed at madhyahnika kalam. It can be done two and a half hours after sunrise. Even if this is not possible, because it must not go unperformed, one can do madhyahnikam after sunrise when the sun is visible.