Is there an Inyan for a father to get an Aliyah for a son (who is under Bar Mitzvah) and a daughter, on the Shabbos before their birthday? Is there an Inyan to get an Aliyah on their birthday if it falls out on a Monday or Thursday?
There is indeed an Inyan for parents to observe Minhagei Yom Huledes on their young children’s birthdays, until they reach an appropriate level of understanding to do so on their own. There were certain cases where the Rebbe advised for the father to get an Aliyah on the Shabbos before (and/or on the day of the birthday if it’s a Yom Kria) for sons until Bar Mitzvah and for daughters.
מנהגי יום הולדת – ראה שיחת ליל ח”י אלול תשמ”ב. סה״ש תשמ״ח ב ס״ע 332. [ולהעיר גם מהיכל מנחם ג ע׳ נה].
לענין עלי׳ לתורה – ראה התקשרות גליון תתקנז ע’ 14.