If I downgrade from Windows 8.1 Pro to Windows 7 Professional, can I change my mind later on and upgrade to Windows 8.1 Pro for free?
Quoting the Microsoft website:
If you do have downgrade rights and decide to use them, you continue to keep the license and rights of use for your original version and may "upgrade" back at any time.
Source: How to downgrade from Windows 8
In short: yes, you can.
Downgrades are not "officially supported" by Microsoft, due to the fact they want you to keep having the latest versions.
To downgrade to Windows 7, you need to disable Secure Boot (if enabled), and wipe the entire hard drive to get Windows 7 to install over top of Windows 8 (or Windows 8.1). Once you made that decision, you need a plan to go back.
Do you have a Windows 8.1 Restore Disk? If so, you can wipe Windows 7 and install the Factory-default version of Windows 8.1. If you don't, then you'll need to "find" a Windows 8.1 disk to borrow, that happens to be the same version as what came on the system. Do you have the CD-Key? If not, it's likely embedded into the BIOS, but only accessible if you have the proper Windows 8.1 DVD.
Can you do it? Possibly. Should you? Not unless you have a technical reason, in my opinion. Remember you also need to make sure you have a legal license for Windows 7 (whatever edition you want to use), and you need to make sure the system manufacturer has the drivers for Windows 7 available; otherwise, you won't be able to use your hardware (i.e. Network adapter, Wifi adapter, your monitor or graphics card at the proper resolution, etc).