Is Zakah(obligatory charity) due on rented property, and how is it calculated?

Zakah isn`t due on the rented property itself, but on the saved income from that property if it reached Nissab(minimum amount liable for Zakah), and a whole lunar year had lapsed over saving it.

If husband doesn`t pray, but wife does, is their marriage contract considered valid or not?

Is wearing a cap permissible for boys, or girls?

In principle, anything is permissible as long as there is no Sharia evidence prohibiting it, thus wearing the cap by boys is permissible as long as it isn`t done in imitation of the disbelievers. Moreover, a Muslim woman should avoid all that which attracts the attention of men because whatever leads to the forbidden is forbidden

Is Aqeeqah due on the miscarried embryo?

No Aqeeqah is due on the dead embryo.