The Ohr Yisrael says that on one’s birthday, it is proper to engage in introspection and seek ways to improve himself(1), Daven for the amud (2), and to give extra money to tzedaka(3)"
1) Ohr Yisroel 24: page 190.
2) Ohr Yisroel 24: page 188.
3) Tzedaka L’Chaim page 35.
Besides these sources, are there any halacha seforim (I.e. Shulchan Aruch, Kitzur Shulchan Aruch or Mishnah Berurah), that mention this?
There are plenty of references. I will bring but a few:
In the Gemara (Yerushalmi, 3, 8) we find that this day has special power. There Rabi Yehoshua ben Levi says Amalek would practice sourcery ... not easily would someone fall on his birthday ... what did Moses do? he suffled the fortunes... (and many Mefarshim provide insight on that Gemara, amongst others the Korban HaEida, the Ramban[1, 379], the Ramchal[Derech Hashem, 2, 7])
Rabbi Haim Palachi (in his book Tzdaka LaHaim) says that in one's birthday he should try to give more Tzdaka (as mentioned in the question)
In Shu"t Ginzei Yosef (mark 4) he states that Anshei Maase would bless Shehecheyanu on new clothings or fruit each year on their birthdays.
Interesting to bring the "Toratan Shel Rishonim" on the Yerushalmi that we mentioned earlier, that says that Jews should not rejoice or have special meals on their birthdays due to the nature of Amalek's deeds on that day (Gonev Nefashot) and further more, the only mention of this in the Tora is the case of Pharaoh (יוֹם הֻלֶּדֶת אֶת-פַּרְעֹה).
In Minhagei HaChasam Sofer, it is stated that he would rejoice in his birthday (7th of Tishrei) and finish the Chumash with his Talmidim and give each a coin in order to purchase milk and bread.
HaRav Yosef Hayim of Baghdad writes in his Ben Ish Ha'i (Parashat Re'eh, Note 17):
יש נוהגין לעשות בכל שנה את יום הלידה ליו"ט וסימן יפה הוא וכן נוהגים בביתנו
There are those who have the custom to make their day of birth into a "Yom Tov", and it is a good sign, and such is the custom in our home
Note 17 continues with the nusahh he would say upon the day he entered Berit Avraham Avinu each year. It includes requests for Yirat Shamayim, to follow the proper path and generally includes sentiments of introspection.
The Rebbeim of Chabad emphasized celebrating personal birthdays. A number of recommmendations are outlined in the sefer הוראות הרבי. They are given by the current Lubavitcher Rebbe as directives for all Jews:
-- One should make a cheshbon tzedek, an accounting of one's righteousness. "On a birthday, a person should examine how he has developed over the past year, so that this progress will serve as a basis and foundation for his continued spiritual growth ad infinitum in all matters of good and holiness."
-- One should take on hachlatos (resolutions) for spiritual improvement and tell family members about them
-- One should make a farbrengen, a chassidish gathering, with good friends
--One should thank H' for his existence, ideally with a bracha (shehechyanu on a new fruit/garment if possible)
Parents "Even the birthday of a very young child should be celebrated. However, this is especially so once a child has reached the age of chinuch [approximately age 3], when he is old enough to be told the significance of his birthday. This should then be expressed in actual good deeds and proper conduct, giving pride and satisfaction to his parents, all of Klal Yisrael, and Atzmus U'mehus [the Essence and Being, i.e., of G-d]!"
Parents are instructed to give tzedakah, increase in Torah study, and reflect on their privilege and good fortune -- and increase their efforts in raising/educating their child to follow the correct path -- on their child's first birthday. Parents should generally observe children's birthdays as a time of celebration, of praise, and of thanksgiving to G-d
Chasidim -- Customs for Chabad chasidim include being called up to the Torah on the Shabbos before the birthday and/or being called up to the Torah on the day of the birthday; giving tzedakah before shacharis and before minchah on the birthday or on the days before/after; studying an additional shiur in nigleh and Chassidus; saying at least a sefer of tehillim; learning his new chapter of Tehillim (that is, corresponding to his new age +1); learning all or part of a chassidic maamar by heart and reciting it before others in public
"Everyone should begin to mark his personal birthday. This will serve as the greatest zechus for her neshamah."
