Is it illegal for me to download DaVinci Resolve 17 just because I don't work for a company?
Yes, it’s ok*, as long as you’re downloading the free version (not the one that says “Studio”) of Resolve and not trying to circumvent their copyright protection.  When you download the software, they ask that you provide some information about yourself so that they can understand their market demographics.  If you don’t work for  a company, just put that, “self-employed,” “hobbyist,” “none,” or similar.  Even if you accidentally download the Studio version (happens all the time, and vice-versa, because both versions are similarly-named), you won’t be able to use it without paying for a license.  You are required to agree to their EULA to use either version.  Ultimately, it’s your responsibility to read it before you agree to it.  Trying to use the Studio (paid) version without paying for it would get you in trouble.  When you do pay for the Studio version, Blackmagic doesn’t require all of the demographic info, although I think you’re required to register the software before they’ll give you tech support over the phone.
*I’m not a lawyer.