Well... in general... I think the important thing is to ask her. Only she knows what will or won't be helpful. Personally I would not want anything "running in the background" with the exception, perhaps, of some quiet music. And I would definitely not want to talk a lot. You would soon find me heading for the nearest door. But that's just me. The fact that people happen to share similar diagnoses doesn't necessarily mean they would have anything in common in terms of how they might want to have a visit go. (I doubt you really needed me to tell you that.)

You asked about discussing depression & suicide. Here again... I would let her guide you. If she doesn't bring these subjects up, I don't think you should feel as though you need to. I suppose you could, at some appropriate moment, say something like: "I don't know if you want to talk about such things as depression & suicidal thinking. But, if you do, I'd be glad to do so. Just so you know..." And leave it at that. Let her take it from there.

There is one additional point, with regard to suicidal ideation, I want to make though. The experts who study & work with this sort of thing tell us that that it's okay & even important to ask a person, whom you believe may be feeling suicidal, straight out... are you thinking about ending your life? You won't put the thought into the person's head. It's already there. And you may just create the opportunity for them to reach out for the help they need.

So... having written all of that, here are links to some articles, from PsychCentral's archives on the subject of what to say to a person who is struggling with depression:

https://psychcentral.com/blog/6-thin...hos-depressed/

https://psychcentral.com/blog/9-best...th-depression/

https://psychcentral.com/lib/best-th...hos-depressed/

https://psychcentral.com/blog/10-thi...sed-loved-one/

Best wishes for a fun & successful visit!