Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.
Is it permissible to recite the Holy Qur'an or to play a recording at mourning gatherings? Or is it considered an innovation?
Whenever Qur'anic verses are recited, it is obligatory upon everyone to listen, otherwise; they should remain silent. And Allah Knows Best.
Is buying and storing gold bars for profit permissible or prohibited?
Buying and storing gold bars for profit is permissible, and there is no harm in it. And Allah The Almighty Knows Best.
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.