Hi there,
I just had a look at my wife's English test certificate and that was in her maiden name and she arrived here with a passport in her married name. Either way she could prove it by photocopying the identification she used to sit the English test. They would not let my wife sit the test without proper identification, thats why she had to use her maiden name as her passport had not arrived by then. They were able to see that it was her from her previous passport which you have to hand in which was in her maiden name. As long as you are able to prove you are that person you will be fine.
On the TB question don't worry about that, that is not needed for the visa application. Although they may ask her for it at the airport as they did my wife. All they do is send you an appointment to see the doctors, have an x ray and they will contact you if there is anything wrong. In our case they never got in contact which sounds the same as what confused me said.