Besides being sane and healthy, does the applicant have to be virgin to be accepted into a religious order?
no, many orders accept widows. you do have to be living a chaste lifestyle, and have no encumbrances, such as minor children who require your care, financial debt etc. Ask the vocations director of the order you are considering about their requirements.
No. You cannot, however, quite obviously, become a consecrated-virgin. But you can become a nun. As mentioned, you would usually be required to have lead a chaste lifestyle for ~2 years though - so you can’t just go from being unchaste and a month later decide to enter the convent without having shown you can lead a pure, chaste lifestyle in the world. However, this may or may not be the case in your own area.