I felt no connection or understanding with my T for the first few months, primarily because I was still hung up on my first therapist and wouldn't let him in. Something shifted after around 4 months to the point I let him in more, but it took a full year before I started to feel attached towards new T and my feelings for T1 became less. It takes time for the pain and trauma of losing a therapist to lessen. Be gentle with yourself.
What I take from your emails is that you are very insecure about the relationship and scared of abandonment, and that is to be expected given what you have been through!
Some therapists have very firm boundaries around out of session contact, particularly during a break, and particularly when the client has been hurt by inconsistent boundaries before.
Let's face it, your former therapist was changing your tyre one minute and telling you he hated you the next! How are you supposed to deal with mixed messages like that, and why wouldn't you expect the same pattern to repeat itself with this T? I bet your T is thinking that it is important for him to model consistent, professional boundaries so that this painful pattern can be broken and you can begin to heal.
That's what my T did for me, and 2 years down the line I'm eternally grateful that I stuck with him.