When creating the export the are many options that can be selected including an option to not include the create database statements ands option to not include comments. you will need experiment with the export settings to find the settings that work for you. I would suggest posting to the HeidiSQL forums with questions about the export settings in HeidiSQL.
"If the site is hosted elsewhere will that matter apart from maybe nano-seconds of processing time?"
it may not be able to connect to the MySQL Server from another location, really depends on the server.
this is one of those try and see type of things that I cannot answer for you, only you can answer it for you.