Have I fixed the run-on?
Thank you very much, Writeacher. I added a few more sentences.
1) John doesn't have to take the car. We can walk to school.
2) Have you received any new emails from my students? How many have you got so far?
3) What are you students learning in Italian right now? Do you think we will be able to start working on a common project before our summer holidays begin?
3. ... your students ...
Everything else is fine, yes!