She's made it very clear she sees you as a friend and has told you that several times. She said you are her best friend and the love she speaks of, in context to everything else she has said, is love in a friendship way. She has tried to be gentle with you, because you are friends, but you are reading things into her actions (probably because it is you that has romantic feelings.) I say this because...
You wanted to date her in the beginning and she said no.
You are wondering where the friendship is going when a friendship can be a final destination many times.
You are thinking you are being played if she dates someone else in spite of her knowing you have feelings for her.

You say you think she is developing feelings for you, but based on what you wrote, the only one with romantic feelings, is you.

To answer the question of whether or not you can have platonic friendship with the opposite sex, the answer is yes. But only if one of you aren't pining for the other. So in your case, however the relationship proceeds, you will be hurt because she only wants friendship, you want more. If anyone is playing anyone, it is you because you continue to pine away for her hoping for more, when she is only looking for friendship.