Any x86 machine that runs Windows 8 will run Windows 7 without issue. The "made for Windows X" stuff is just marketing fluff.
I'm sorry, but that is not
Windows 7 will install on any laptop that supports Windows 8 or 8.1, yes, however there's no guarantee you'll have drivers available for your laptop that are compatible with Windows 7. It is strictly case by case, I'm afraid. Browse the stores carefully and check the manufacturer's website for any model you're interested in buying. If they offer driver downloads for Windows 7 on that model, then you're fine.
If they don't have Windows 7 drivers, take a careful look at the provided Windows 8 and 8.1 drivers to see whether you can identify who makes the individual components. If you get lucky, they may be made by companies that provide generic Windows 7 drivers on their own website. There's no guarantee those generic drivers will work, as laptops are usually not fitted with completely stock parts, but there's a good chance that they'll at least provide baseline functionality to the system for your components. You'd have to check every component in this case, and see which ones offer drivers and which ones don't. For any components that don't have drivers you can assume they'll just not work under Windows 7, but that might not always be a bad thing as you might not want to actually use the fingerprint scanner or the webcam. Still, you have to be through and make these decisions for yourself.
Ultimately, it's just easier to buy a laptop online from a reputable manufacturer that offers good shipping options and the OS you need. About the only thing most websites won't tell you is whether the screen is glossy or matte, and whether it's an IPS or TN display. Otherwise, the reviews will probably tell you everything you need to know about a particular model, so be sure to read those before committing to anything.
Still, you can't just buy any Windows 8 machine and just hope it works out alright, you've got to do your research. You know, unless the store has a ridiculously good return policy.