While I'm no particular fan of your T, I think she is actually being more generous than a lot of Ts would be in responding twice to an e-mail that you sent between sessions, when you see her twice a week-- and she hasn't been paid to see you for months. Many Ts will not read/respond to e-mail at all. Doing therapy in person really is more effective. Not to mention that Ts need a little free time-- if they have to read/respond to e-mail every day, after a full day of seeing clients, and they don't get paid for it-- it can be a lot of added work and stress.

Is asking your T to go "above and beyond" for you (e-mails, ten extra minutes, etc) really a way of asking her to "prove" that she cares about you? Do you think if she does X or Y, then that will allow you to believe that she likes you and wants to see you? There isn't really any reason why she needs to respond to the e-mail (it really deserves an in person conversation, and youre going to see her Monday) and you don't really need ten extra minutes (your sessions are often filled with lots of silence and difficulty finding things to say to each other). So, at least from the outside, it seems like maybe your requests are really a way to get her to do something to prove that she WANTS to see you and cares about you?