Some of the things you've talked about feeling are "common courtesy" and you felt the T was rude or even hostile for not: saying hello, asking about your trip in, offering water, walking you to the door, shaking your hand.

I was also brought up with a more strict interpretation of common courtesy/polite behaviour than is common these days. However, I have found that leading by example will often elicit the response I want. It's fairly automatic for most people to respond if you say hello or goodbye.

What would happen if you went in and were the one to initiate conversation ("hello, it's good to see you - how was your morning?")? She's not going to tell you about the details of her previous clients, but she might well say "my morning was alright, what about yours?"

You want her to offer you water... next time, bring two bottles of water. Pull one out of your bag for yourself and offer her the other.

At the end of the session, stand up, thank her for her time and offer your hand. She's unlikely to turn down a handshake or to be rude in response to a polite closing statement.

I suspect you'll respond to these suggestions by saying it's not your responsibility - she's the professional, she's supposed to be welcoming you into her office and doing her best to build rapport. I would argue that one should always be polite, regardless of the position of power you're in. Additionally, since it is easy to influence this level of behavior in many people, if it is important to you why wouldn't you do it?

Finally, there is a saying among therapists: don't work harder than the client. It sounds like you're upset because perhaps that's what this therapist is doing. She's not pushing herself to change her behaviours to make you comfortable and you're not pushing yourself to change your behaviours (trust her, accept her) to do the work that needs doing.