I would be very upset if my T was texting during my session and it wouldn't matter if it was to another client or to a family member... Then I would expect the explanation because I guess emergencies can happen so once or two I would forgive but continuously?

I agree however with 1914sierra that most of this what you've written were your "impressions", do you think that you could confront your T regarding them? And tell your T how you feel when he's texting others but you don't get the response from him for days etc... If you really do not like his approach maybe finding a new T wouldn't be so bad idea...