Thanks for these questions. First, yes, though I don't know anything more about you than your questions indicate, it is entirely possible that you are called to contemplative life and mystical prayer. While we don't hear a lot about mystical prayer today, it does exist and (if you know the right people!!) is a vital stream in the contemplative tradition today. Our church stresses apostolic ministry today more than contemplative life and most folks will find themselves involved in active ministry with prayer lives that support them in this. Some of these, especially religious women and men, however (the group I know best perhaps), develop strong contemplative prayer lives to anchor their active ministries and more, to fulfill their vows and vocation as religious. Many of these I think, especially as they age and "retire", allow themselves to focus on developing their contemplative prayer and some of these (perhaps a significant number even) will move through the various stages of prayer Teresa of Avila, for instance, outlined. Their prayer becomes profoundly mystical as God draws them ever deeper into His own life and heart. And then, of course, some of us are hermits!!
Since you asked, however, no, you don't need to be a hermit for this (though I personally find it a natural context for growth in contemplative life and mystical prayer), and while I think you could well be married, I personally believe it might be difficult to manage both loves at once. Again, this is a personal opinion; I am not sure about this since I know women religious who manage their community and ministerial commitments just fine, along with some significant friendships, even as they pursue the deepening of contemplative and mystical prayer lives. My one suggestion to you is that you find a good spiritual director with whom you can work regularly. S/he should be essentially contemplative and knowledgeable about working with contemplatives at various stages of prayer, especially if mystical experiences are a part of the directee's prayer life. At the very least, s/he should be open to accompanying someone in and through such stages and expressions of deepening contemplative prayer; this requires a specialized kind of experience and learning both in prayer and in spiritual direction. Remember that mystical prayer is, first and last, about one's relationship with the Mystery we know as God (in Christ); a director should be profoundly rooted in such a relationship herself (or himself).If there is a Carmelite Monastery near you (or relatively near), you might check with them and see if any of their Sisters or Friars do spiritual direction. Of course, other congregations will be able to assist you in this matter as well; apostolic congregations tend to nurture contemplative prayer these days as well. What is true, however, is that not every person doing spiritual direction today will have either the experience or the education and training to accompany you if you are truly called to mystical prayer. (Note that each one of us is called to union with God which implies we are each made for mystical prayer; it is not, however, easily cultivated and/or a gift easily received.) You are looking for someone who can accompany you in direction for some period of time, and who can assist you in discerning the movements of the Spirit, but especially as these are evident in invitations to greater depth and intimacy with God. Such persons would be able to accompany you even if you discover you are not called to contemplative life or mystical prayer.