Can I share my form with others so they may edit it and use for their own purpose?

Yes, you may share the form link as well as the guide so they can clone the form in their account and use it as they want, these guides will help you doing so: 

https://www.jotform.com/help/401-Where-to-Find-My-Form-URL 

https://www.jotform.com/help/42-How-to-Clone-an-Existing-Form-from-a-URL 

You may also share it as template so others can use it, here is the guide: https://www.jotform.com/help/157-Sharing-a-Form-in-the-Form-Templates-Gallery 

I hope this helps.