Sorry to post it here but unfortunately I can't post in the relationship forums yet

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so my problem is I have been seeing a woman for approximately 2 months! I've not met anyone like her in a long time and she drives me wild as she plays aloof and hard to get so much!
My issues are the following and I would appreciate any input anyone has ... good or bad!
1)As pathetic as she sounds she wont allow me to be her facebook friend. Now a while ago I added her and she said "do you need to part of every part of my life ... "so I removed the request and when the issue came up again I laughed and said "I only give you one opportunity to be my facebook friend" jokingly. Should I just leave this or?
2)She Brings up past relationships/”lovers” for example she has recently been traveling and bought up a friend who lives in another country saying we should both go out and visit him, and then said "actually you probably wouldn't get on" so I know she has slept which him, which isn't a problem it's in the past but the question is whether I should let her go alone if she wants or go and meet him and play it cool ... at the end of the day she is seeing me now not him?
3)Friends make fun of her because she won’t call me her boyfriend – I make light of it by calling us partner 1 and partner 2 and also jokingly asked if she would be bothered if I went off with other girls then with what she replied "well I wouldn't see you again". Again, should I leave the boyfriend/girlfriend issue? at the end of the day do we really need to have a title a long as we are commited to each other?
4)Her longest relationship is like 4 months as she says she always panicky! Again I try and laugh this off and joking say well I usually get bored after a couple of months so you've not got long left!
Has anyone got any advise and guidance on girls such as this!? Ones that are scared of commitment and so on? I know it's only been two months!
Thanks in advance all