Sometimes they just need to have a person who lets things be normal - someone who knows what is there, but doesn't let it change the tone of every interaction.
That seems one of the most helpful things you can do, in my opinion.
Often, you're right, it would be fantastic to just hear from someone who invites themselves over for lunch and a game on the weekend. Other times, you really want to be able to just have a deep conversation with someone, to be able to let your guard down for a while and talk about troubling things openly and honestly. Unfortunately, that's often unrealistic: the other person has to be in the mood for it, you have to feel safe enough about it to not shy away from it because it might be made a big deal of later on, when you're feeling better.
Yes. I'm very glad you said this. Mental illness is bad, but even worse is all the nonsense you have to put up with from people when you try to get your life back together-- the prying questions, the discrimination, the ridiculously long-lasting career-altering properties (due to people in power generally being superficial and mean-spirited) of minor health problems.
It's like a hurricane. A few people die in the storm itself, but then hundreds or thousands die in the human-made chaos and disintegration afterward. Seeing the wreckage that is made of your life after a mental health event (and experiencing the fact that many people want, with glee, to push you back into the hole, because it means less competition) can, for many people, trigger another one that is longer-lasting and harder to break out of.
If you're not a psychiatrist or therapist, often the best thing you can do for a mentally ill person is help that person get back to a normal life.