I think that your new T isn't expecting to be received with wide open arms immediately, so these 2 may be unnecessary to refer to:

1. You cannot fill my therapists shoes.

2. Dont expect me to accept you with open arms.

With #3, I would like to gently remind you that different T's have different demeanor. Some are real bubbly, others are more solemn. I think that most take their cues from the person that they're working with. If these types of behaviors offend you, and make you feel really tense, maybe you should sum it up that way. Saying:

"I really don't do well when people make jokes. Please try to remember that in the future."

#4 is good the way that it is, I think.

#5 ~ I agree with the others that this should be changed from Don't do this...to:

"I really have a difficult time with the list of words that I've given you. Please don't ever use that terminology with me. Use these words instead." Hopefully, you have some words that you are okay with, that have same/similar meanings.??

Numbers 7 & 8 should also be made about yourself.

"I have a hard time trusting another to feel safe enough to open up. Please be patient with me. I am not easy to read, wearing my emotions for everyone to see."

I think that covers it all. That's what I recommend...jmo.