На мой взгляд, тут в большинстве случаев возможны оба варианта :)
1. My mother will go / is going to go to the first meeting with me - возможны оба варианта.
2. She will meet / is going to meet - возможны оба варианта.
3. I am going to / will take flowers for her. - возможны оба варианта.
4-5. I hope it will not rain as I will wear / am going to wear a new dress.
6. ... I am going to be a fashion designer.
7-8. I hope my new classmates will be friendly and we will have a great year together.