If I have an active download and I stop it, will it resume from where it left off when I connect the Internet again?
First open FDM, right click the entry of the file and click stop. Now you can shut down the computer. When you want your download to start, right click and click start.
This depends entirely on the resume support capability configured on the server where the files are. Some websites are configured to allow resume support, others don't allow it but you can add links to the download list and then download them whenever you want.