How do I embed my form into emails to Clients and how do they email the completed version back to me?

It's not currently possible to "embed" your form into emails because most email systems only support html and it would then lose most of its functionality.

However, the best way around that issue is that you can add a direct link of your form for your emails to send your clients. They could click on that and it would take them into their browser where they would be able to fill in your form and submit the data back to you. At that point you could have an email notification which you created which would send your information back to you.