Can I install older macOS verisons on a newer computer (and a newer version of macos)

Hi all,

After 7 times of trial and error, I finally was able to Hackintosh my Laptop. But the thing is I was able to install Catalina but I wanted to install Mojave because it suits my needs and supports 32-bit applications. But my laptop came out after Mojave so is that a problem or not? I have an i5-1035G4, if you need to know more of my system specs, please lmk

Also another question, if I can't install Mojave, can I update to Big Sur through the app store or do I have to go to my com.apple.recovery folder on my USB and replace the Catalina Recovery files with Big Sur with GibMacOS?