Is it permissible to offer mandatory prayer while sitting?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.                                                                                                                                                                                                                            Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.

Is a woman's prayer performed while following an Imam whose prayer is being broadcasted via the television valid, and does she receive the reward of congregational prayer?

I`m a pious Muslim woman, but my husband isn`t, what should I do?

You should exercise patience, make supplication that Allah guides him to the straight path, and keep advising him kindly.

Is it permissible to delay the ritual purification (ghusl) from major impurity (janabah) until after dawn?

Yes, it is permissible to delay ghusl from janabah until after dawn, as purity from janabah is not a condition for the validity of fasting. However, one must perform ghusl in time to pray Fajr within its designated time.