Hi! Welcome to the forums. I am not a teacher.
Here's my two cents.
1) speak+ language
eg. I speak Chinese.
eg. I talk Chinese.
2) Phone Calling
eg. Hello! This is Mary speaking.
eg. Hello! This is Mary talking.
3) speak: deliver a speech in a meeting
eg. He spoke at the meeting yesterday.
4) speak of sth/sb
5) speak to sb
6) "talk" focuses on mutual dialogue
eg1 What are you guys talking about?
eg2 Anglika is talking to me.
7) "speak" focuses on the act.
Hope this helps.
Student or Learner