how to check if she has seen my messages on fb?

[pri✍]

You'll know if she read your FB message in her Other folder if you see "Seen at...." at the bottom of your last message, unless after read it she Mark as Unread. If she still YM you, if she saw & read it, most probably she'll answer you.

I suggest for you to add her as friend, therefore, she know you contact her & your message will go to her Inbox, ask for her email address so you can email her.

There are also many ways for you to communicate only to be seen by the two of you, beside FB Message, in Facebook.

You can then ask her to hide her Friends list, so her family/friends will not know that you're her FB friend.

Regarding your YM, maybe you can upgrade it, no way you can receive her message but she can't.