Praise be to Allaah.
In Islam there are only two celebrations, namely Eid al-Fitr
and Eid al-Adha; anything other than these two celebrations is an innovated
festival or occasion and it is not permissible to celebrate it or to help
others to do so.
The scholars of the Standing Committee said:
It is not permissible to celebrate the occasion of Laylat
al-Qadr or any other night, or to commemorate other occasions, such as the
night of the fifteenth of Sha‘baan (laylat an-nusf min Sha‘baan), the night
of the Mi‘raaj (Prophet’s ascent to heaven), and the Prophet’s birthday
(Mawlid), because these are innovations that have been introduced into Islam
and that were not narrated from the Prophet (blessings and peace of Allah be
upon him) or from his Companions. The Prophet (blessings and peace of Allah
be upon him) said: “Whoever does an action that is not part of this matter
of ours (i.e., Islam) will have it rejected.” It is not permissible to help
others to hold these celebrations by means of money, gifts or distributing
cups of tea, or by giving speeches and lectures on these occasions, because
that comes under the heading of approving of them and encouraging them.
Rather one should denounce them and not attend them.
End quote from Fataawa al-Lajnah ad-Daa’imah,
Based on that, it is not permissible for you to make cakes
for these and similar occasions, because that comes under the heading of
helping others to celebrate them. Celebrating them is not permissible, so
helping others to do so is not permissible either, because of the general
meaning of the words of Allah (interpretation of the meaning):
“Help you one another in Al‑Birr and At‑Taqwa (virtue,
righteousness and piety); but do not help one another in sin and
transgression. And fear Allaah. Verily, Allaah is Severe in punishment”
The scholars of the Standing Committee also said:
Exchanging gifts is something that creates love and harmony
among people, and dispels resentment and hatred. It is something that is
encouraged in Islam; the Prophet (blessings and peace of Allah be upon him)
used to accept gifts and reciprocate, and that is something that is commonly
done among the Muslims, praise be to Allah. But if the gift is accompanied
by a reason that is not acceptable in Islam, then it is not permissible,
such as giving gifts on the day of ‘Ashoora’ or in Rajab, or on the occasion
of birthdays and other innovated occasions, because that is helping in
falsehood and participating in bid‘ah (innovation).
End quote from Fataawa al-Lajnah ad-Daa’imah, 16/176
Making a cake and giving it to the child on this day, and
telling him that this is his birthday so as to make him happy, comes under
the heading of celebrating, even if his family do not call it a celebration.
Undoubtedly celebration may take many different forms, but this does not
mean that it is permissible. They have only chosen this day to give the
child a gift because in their hearts they feel some love for this occasion
and are trying not to let the day pass without celebrating it, even if that
is only by giving a gift to the child.
And Allah knows best.
Please see the answer to question no.