Is it permissible to combine the intention of fasting the White Days or days from Rajab and Sha'ban with the intention of making up for missed fasts of the deceased mother, and making up for the missed fasts of the questioner due to legitimate reasons that were not made up, and is the fasting of the questioner from the age of 8 considered making up for what she missed, knowing that fasting begins at the age of 9?

If your deceased mother was able to make up her missed fasts but did not, it is recommended to fast on her behalf. It is not permissible to combine the intention of fasting the White Days or some days of Sha'ban with the intention of making up fasts for your mother, nor to combine them with the intention of making up fasts for yourself. As for fasting some days of Rajab, it is permissible with the intention of making up fasts for your mother or for yourself, without combining intentions.

Fasting becomes obligatory for a girl when she shows signs of puberty. Your fasting at the age of eight does not count as making up missed fasts, because it was a supererogatory act before puberty. After puberty, whatever you fasted as an اداء (performance of an obligatory act) counted for that obligation, and whatever you fasted as a supererogatory act occurred before you stopped fasting and lacked the intention of making up missed fasts.

Therefore, you must make up the obligatory fasts you missed. If you do not know the exact number, continue making up fasts until you are reasonably certain that you have fulfilled your obligation.