1. Is a "God-pleasing, platonic relationship possible with someone you've had feelings for in the past?"  Yes, it is definitely possible.  I have been able to create some great friendships with those I've had feelings for.  However, it has taken a great deal of time away from each other, distance apart from one another and a concerted and deliberate effort (with personal and spiritual guidelines) in order to build them. 
    In your case, the friendship (using the term loosely) does not sound as if it is based upon trust and honesty, nor does it seem to have a strong spiritual basis upon which it was developed.  It sounds as if she wants to have a friendship "with privileges."  Why would you want to put yourself (or allow yourself to be used) in that sort of situation?  You are better than that, to yourself and to God.
  2. Is she a "player"?  I don't like to put labels on people and classify them into a group.  However, if she is saying the things you want to hear, is leading you on with her actions, has no feelings for you and you are sticking around, you are being played
    It may feel good for that moment to be (temporarily) desired by the person you have feelings for, however, if she is saying these things to you, what do you think she is saying to her "boyfriend" who she "loves" or to another "friend" of hers?  If you ever did have a relationship with her, do you think her lack of openness and honesty will change or will she carry on other "friendships" during your relationship?
  3. It is great God is using you in your friend's life spiritually, but she doesn't need a male friend (nor does her boyfriend probably want you to be) who she confides in.  Direct her to a mature female who she can share her past and issues with.  It sounds as if she may be reaching out in an effort to be loved and desired for something she may have missed growing up.
    You won't be abandoning her, but rather directing her to someone who is in a better place and position to help her.
  4. Your heart still seems emotionally connected to your friend and you need to be cautious to not "rush" into anything, especially when it involves another person's feelings.  Unless you can wholeheartedly give yourself to someone or something, you should consider waiting until you can.

Whatever you do, work at it with all your heart (Colossians 3:23).

Pursue someone you fully want and feel led to have a relationship with.  Don't chase someone just because they showed some interest in you.  Relationships are hard enough when both of you are trying, so don't begin one unless you are fully committed.

Whether we acknowledge it at the time or not, we often receive God's direction through his Spirit.  Our human feelings, desires and "knowledge" are the things that often get in the way with thinking clearly and hearing his voice.  Continue to seek him in all you do.

SHE SAID:  I'm thankful.  Yes, that may seem like a bizarre way to start out answering your question.  But I really am.  I am thankful that you are seeing this situation for what it is, and that it has helped highlight some issues in your own life that you wish to work on and hopefully will learn from going forward.

I do believe God allows us to make mistakes, to trip and fall, to find ourselves in a mess of our own doing.  And thankfully (yes, thank you, Lord!), he does not hold our wandering ways and transgressions against us (Psalms 103:10-12).  Believe me, I have been there myself and am not casting stones at all (Some of us have to learn the hard way, right?  And it's good to take a closer look at what we have done and why.).  It's not a great place to find yourself, but when you've hit bottom (in any type of situation) then there's no place else to go but up.  We can either choose to stay in the pig-pen of poor choices or we can receive the Father's outstretched hand, stand up, dust ourselves off and start walking toward a way of living that honors him (Ephesians 4:22-24).

After taking part in a relationship such as this, I'm sure you will be more aware and mindful of your future interactions with women who are already in relationships with others.  I've read before that it is a good policy to regard every man or woman (those who are single) as though they are already someone else's husband or wife—primarily so that you will guard yourself and your actions, treat them with respect and honor and not be led into temptation or into any sinful behavior (James 1:13-15; 1 Corinthians 10:32-33).

Due to the length of your inquiry and questions, I can tell that this situation has greatly affected you and that you have been convicted of your choices and corresponding actions.  I believe you are gaining clarity and are moving in the right direction. 

So let me answer your four questions: