Is prayer obligatory upon a wife during intermittent bleeding throughout pregnancy, and is this blood considered menstruation that exempts her from prayer? And if it is not menstrual blood, what should she do regarding the missed prayers?

The bleeding mentioned is not menstruation (hayd) but rather irregular bleeding (istihada), because, according to the most authoritative opinion, a pregnant woman does not menstruate. A woman experiencing irregular bleeding is considered ritually pure, so prayer and fasting are obligatory for her, and it is permissible for her husband to have intercourse with her. She must perform ablution for every prayer. What was obligatory for the wife was to pray and to ask. Now, she must immediately make up the prayers she missed, to the best of her ability.