Can you place the token into the URL query string? - If yes, How?
Not sure what you mean with this exactly. But given that you are a call center, I assume you want to get around the email invitation.
This is possible. Once you have a token table, go to this token table and if you click on the little wheel you will see the link for the survey, how it looks like and where the token comes in. Based on this template you can create links including the token via Excel. I described that once in the manual, but I couldn't find it lately, probably someone reworked the manual and deleted my workaround. Have a look, maybe you'll find it.
The second question is also possible. Set "token based response persistance" to on and when you open the link (no matter from which computer or who does it) the survey should start from where the survey was left off (of course only to the point that was sent to the database, so everything entered to the last open page without submitting will be lost).
As long as the token is different for each person, you should be able to run your operation as you wanted to.