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).
Who are the blood-relatives with whom kinship ties should be maintained?
Blood-relatives are those from the side of one`s father and mother: grandfathers, grandmothers, uncles, and aunts. And Allah Knows Best.
Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
What is permissible for the husband to do as far as having sex with his wife is concerned?
The couple are free to enjoy each other sexually provided that they don`t do it during menses. It is also forbidden for the husband to enjoy the wife from her anus.