The phone thing has been addressed well by others.

Honestly, my biggest concern is her handling of your suicidality. This is a fairly common problem for me, and if my T handled it like that, I'd probably be dead. Now perhaps you haven't given us all the details, so if she goes beyond talking about her friends (which honestly doesn't seem appropriate for the seriousness of the concern), perhaps it is okay. Is she asking very pointed questions to find out the level of your suicidal thinking/intent/planning? She should be. Is she giving you some concrete steps for you specifically (beyond just telling you a story about her friend) that she wants you to take when these thoughts come into play? She should be. She should be setting up/discussing who to contact, at what point to make contact, how to know when this has gone beyond thoughts and into an emergency, etc. Even if you don't have plans now, not discussing that possibility is like the elephant in the room, and that elephant doesn't belong in a therapy session.

My gut, if we have the whole story, is that you may very well be right. She comes off as flighty and inexperienced. Might be time to move on.