Should a woman who broke her fast because of delivery make up for missed fasting days before the next Ramadhaan, and what is the expiation due on her in case she delayed making up for them ?

She should make up for missed fasting days before the start of next Ramadan if possible, but if she didn`t while being able to, then she is obliged to make up for them along with feeding a needy person for each delayed day of the missed fasting days. However, if she wasn`t able to make up for the missed fasting days before the start of next Ramadan, she has to fast a day for every day that she missed, and no ransom is due on her. And Allah Knows Best.

Is Fajr (dawn) Sunnah a confirmed one?

All praise be to Allah The Lord of The Worlds                                                                                                                                                                                  Of course, it is a confirmed Sunna which the Prophet (PBUH) used to offer in a regular basis. And Allah Knows Best.

Ruling on combining prayers in a marketplace due to heavy rain, knowing that some people performing prayers are customers?

Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?

It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).