Can you please have a look at these few sentences? I urgently need to know if they are right.

1)It would be nice if my students from the ninth class could start emailing to your students to practice their English.
2) They already keep a diary about their daily routine so it would be nice if they could exchange their experiences with yours.
3) By the way, one of them is Swiss, others are Rumanien but all of them are really interested in making friends with your students.
4)My father is diabetics.He has to test his blood sugar levels regularly.
5) My mum tripped over a stone when she was walking at the zoo and broke her wrist. The surgeon put it in a cast and she had the cast for a month.
(She had the cast removed yesterday).

6) The other day I slipped and fell backwards/over (what is the difference) and banged my elbow on the ground.
My arm was bruised./I had a bruised arm.

1. omit "to" before "your students"

2. OK

3. ...one of them is Swiss, while others are Romanian; all of them, however, are ...

4. diabetic
blood-sugar level
(no plural endings should be here)

5. OK

6. OK
falling backwards = just that, falling so that you land in back of where your feet are
falling over = falling forward or slightly to one side or the other