I don't think there's a baseline therapeutic relationship. Each therapist is different, each client is different, and each relationship is different. So it may take some time to find out what works for you and your therapy. It takes communication and talking things out.
In terms of out of session contact, again that's going to be depend on your therapist. Mine allows me to e-mail me, but she generally won't respond. She also made sure that I understood that e-mail isn't secure and that she can't guarantee my privacy when I send her things or when she does reply.
It sounds like you had some minor miscommunication. You didn't make a mistake or overstep any boundaries. If you can let it go, great. If you want to talk about it with your therapist, that's great, too!
Good luck on your journey!
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Be who you are and say what you feel because those who mind don't matter and those who matter don't mind.
~Dr. Seuss