If you want to write a good mixed sequence paragraph, you need to be aware of what in the paragraph you are trying to say, and how the things should coordinate with each other and with the general idea of the paragraph. In order to get a good paragraph, mix the basic listing of ideas in a paragraph with sequencing and coordinating them in an interesting way and you're sure to get an interesting paragraph.
Yes. The sentence with correct parallel structure would be as follows. The doctor known only that her patient would improve, but also knew that her patient would [can't understand the sentence after that, but nevertheless it is still faulty].