I don't think that FileMaker can automate the entire process on its own.
You can definitely automatically create and send emails from FM - use Send Mail (via SMTP Server) script step.
For automating the replies, you can include a hyperlink in the email so that when the reply is received, in somebody's inbox, the email can be opened (manually), the link clicked, and that link will fire a script in a running FM solution. Use the fmp:// protocol to create this link.
I suppose this relies on the reply containing the original message.
There are many ways that you can accomplish this. I wouldn't recommend having your users answer the questions by replying to an email sent from the database. Parsing out answers gets real tricky and is more trouble than it's worth.
In addition to David Moyer's suggestion, another option is to publish the timesheet via WebDirect. This way they can submit their response in a browser and don't need to have a copy of FileMaker. An email from the database could be automated using a server-side script (nb, requires FileMaker Server), and can include a personalized link that can create a record in the database for that user.
There really isn't a super-simple approach that won't require at least intermediate-level scripting knowledge. These types of projects are great for learning, or you can always contract it out if you need something done quickly and professionally.