Is eating ‘ashoura at the day of ‘ashoura (tenth of Muharram) considered bid’a? Is it permissible to eat this sweet a day before or after the tenth of Muharram? What is the ruling on spending extra during my birthday, by buying fruits and sweets, with no celebration held for this occasion?.

Praise be to Allah.
Firstly:
If this food is some of the Shi’ah food that they make on ‘Ashoora’ along with the cheek-slapping and hitting themselves that they do, then it is a reprehensible innovation that the Muslim must keep away from and not participate in it. We have quoted the fatwa of Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him) in the answer to question no. 102885. But if this food is not accompanied by those things and the aim is just to treat oneself and one’s family, then there is nothing wrong with that and it is not described as a bid’ah (innovation).
Many scholars have stated that one should treat oneself and one’s family on the day of ‘Ashoora’, and several ahadith have been narrated from the Prophet (peace and blessings of Allah be upon him) concerning that, but they are all da’eef (weak) and are not saheeh (sound).
Secondly:
Celebrating birthdays is a reprehensible innovation.
Eating food treats on that day and bringing sweets and fruits is a kind of celebration and veneration of that day, and should not be done.