To install XP Mode in Windows 7 Pro, you need to also install Windows Virtual PC.
Given the age of Windows 7 and XP Mode, the download links in most of the online XP Mode installation guides are no longer valid.
Download the Windows Virtual PC here, being sure to select 32-bit or 64-bit as appropriate for your installation of Windows 7 Pro: https://www.microsoft.com/en-us/download/details.aspx?id=3702
For completeness, the download for XP Mode is here (you almost certainly do NOT want the "N" version): https://www.microsoft.com/en-us/download/details.aspx?id=8002
You do NOT need to keep Firefox open. In fact, unlike Internet Explorer, Firefox should just save downloaded files and not ask if you want to "run" the files as they are downloaded. If you are not sure where Firefox saves the files it downloads, click the menu icon (the 3 horizontal bars at the top right corner of the Firefox window) and select Library > Downloads > Show Downloads Folder. This will open a Windows Explorer window showing the folder where your downloads are saved. You can now close Firefox (although leaving it open won't harm the installation).
Once you have downloaded both installation files, follow the directions here: https://www.bleepingcomputer.com/tutorials/use-windows-xp-mode-in-windows-7/
Note that connecting XP Mode to the Internet is just as dangerous as connect a non-virtual installation of Windows XP to the Internet. Neither will update beyond the security patches available as of April 8, 2014, Most, if not all, current antivirus programs will not run on XP.