That does sound like a promising lead!
That's a good question about trauma informed care! So, yes, in theory all therapy should come from a trauma informed approach. But for a long time, a lot of therapeutic practices on both an individual and institutional level didn't really structure themselves that way; not in the sense that they were trying to re-traumatize clients or that they ignored or disbelieved their trauma (though that certainly still happened), but more in that they didn't look at all the ways trauma could be re-triggered. For instance, a lot of therapy used to be very one directional; the therapist is the expert, they tell the client what to do, and might even penalize them in some way for being "non-compliant." A trauma informed approach acknowledges that clients who have survived trauma need to have power in the interaction and be treated as the experts on their lives. I think this offers a good break down of what the term is meant to cover: http://socialwork.buffalo.edu/social-re ... -care.html
I will say that trauma informed is also considered a standard of care now, bordering on a buzzword, so a lot of providers use it to signal "I am up to date on best practices."
As for your second question, that is absolutely a reasonable thing to tell a therapist. In fact, it can be really helpful information for them to have, because they know that a) you have some bigger stuff you'd like to discuss down the line and b) what you're comfortable bringing up as you build a therapeutic relationship with them. I also think it serves as a good "test" of that therapist; if they react poorly to you setting a needed boundary, that's a sign they're not a good fit.