Is it permissible for a woman to pray in what is called a "shirshaf" or "jalab" (a large, loose garment covering the entire body), given the belief that it is not permissible to designate a specific garment for prayer?

If the sheet or jilbab covers the entire body and is not transparent, then it is permissible to pray in it. However, if it does not adequately cover the 'awrah, then the prayer is invalid, because covering the 'awrah is a condition for the validity of prayer. As for dedicating a garment specifically for prayer, there is no harm in it; in fact, it may be recommended for a breastfeeding woman and those in her situation.