What does "dawning way" and "tin machine" mean in the context below?

Elizabeth walked up and down on the shiny tiles. She did not like people

to observe that she was being kept waiting, and at least one girl was smiling

at her in that shy, dawning way which meant she had seen Elizabeth on TV;

but there was no decent coffee to be had, and no civilised place to sit. She

measured her pulse on a tin machine outside the chemist shop. The reading

she got was so low that she thought the thing must be out of order.