How does or would your therapist respond to expressing anger towards them?
He usually thanks me for telling him. He doesn't get angry, he expresses that he's sorry that I was hurt by something, and if he's done something wrong he'll apologize for that and accept responsibility (sometimes I'm angry and completely aware of the fact that it's irrational and he has nothing to apologize for)
The way he completely mishandled terminating was the source of a great deal of hurt for me and I've been angry about it a lot. Like he really ****ed that up. He acknowledges that he ****ed up. Even almost a year later I still get angry about it again, and he gives me space to be angry and I never have to worry that he'll retaliate.
A while back I wrote an angry journal/letter to him that I brought to a session. I prefaced it with all kinds of disclaimers, that it was angry and parts of it were written to be intentionally hurtful out of anger, and so I felt like I "shouldn't" let him read it. But, on the other hand, those feelings were affecting therapy and how I felt, and thus I felt that I "should" share them. After I finished rambling, having overthought this by like several meta levels and been unable to come to a decision, he said he would want me to share it and said "how about you be responsible for your own emotions and feelings, and I'll be responsible for mine," basically wanting me to trust that he could handle it.
He thanked me for sharing it, said he wanted me to tell him when I'm angry, accepted responsibility for the things he did wrong, acknowledged my hurt, etc.
Oh, and early before the disclaimer when I first told him I was angry he requested that I look at him during that conversation. I think he was glad to hear me finally allow myself to admit I was angry about something.
I wrote about the session on here, but it's quite long and not really that interesting

Have or could you tell your therapist you hate them?
Nope. But that's not about him. I've never told anyone that I hate them out of anger, and it's actually something that I resolved to never do when I was quite young.

Is raising your voice in session acceptable?
To some degree, but not screaming. I also think dynamics matter. I'm a 5'5" woman who is pretty much as non physically intimidating as possible. If it were reversed it would be a different.

Do they allow angry phone calls between sessions? Angry emails?
Nope. Communication between sessions is only for practical matters, scheduling and insurance stuff, so it's not about the anger.

Have you ever accused your therapist of hurting you? Or not caring? Or not being competent? Could you?
Of hurting me, yes, and it was true and completely warranted. If I'm hurt but he hasn't done anything wrong then I'll explain that.
Of not caring, yes. But it's not really something I say while angry, it's usually explaining the thoughts I'd been having at some previous point in time when it felt much more believable.
I've said he made the wrong decision about something and even gone so far as to say it was irresponsible and he should have known better, but it's only been about specific things he did, not generalized about him as a person.