Example 1: Hope you are doing well and the meeting with your doctor goes well!
Changed to: I hope you are doing well, and that the appointment with your doctor goes well too!
You need to identify yourself in this sentence as I. Also, an Oxford comma breaks up sentence flow better, and the too at the end implies that you would like both of these to happen. Also, if you are going to see a doctor, it's usually called an appointment, or doctor's appointment (thanks, itsraghz)
Example 2: Could you recall me the name of topic of other group?
Changed to: Can you recall the topic names of the other groups? OR if there is only one group and not multiple groups, Can you recall the topic name of the other group?
You can swap Can for Could at the start of both sentences. Could is more formal, but also more literal, in that the ability to recall is being stressed by the sentence, whereas Can, which means basically the same thing, is often used as a simple inquiry or request and only occasionally stresses the ability to do something.
Example 3: Could you also give me some name of other topic that not took it yet by student to choice one of them
Changed to: Could you also give me some names of other topics not taken yet by students so I can choose one of them?
In this sentence, you've missed the plural form of name(s), topic(s), and student(s). I also changed to for so I can as to give a coherent explanation for the request. Also, don't forget the question mark at the end!
I hope that clears up most of your syntactical questions, regarding this email. Please remember plural forms of words! They are very important. If it's more than one, there's usually an s at the end of the word to indicate that it is plural.