First, NEVER run yay as root. Never. Just don’t do it. Don’t run sudo yay and don’t run su first and then yay. yay does not need root access, and should not have it when building AUR packages. When yay needs root access, to install something, it will ask you for your sudo password.
Second, there is no need to type yay -Syu, just run yay, it does the same thing.
Third, it seems your repo packages are up to date, and you only have the AUR packages to update. Whenever you’re updating an AUR package, you should do the same procedure as when installing it, check the PKDBUILD and all.
When you are asked
Remove make dependencies after install?
you can safely answer either yes or no. Make dependencies are packages that are needed to build the AUR package (like compilers for various languages, libraries, etc…) but they are not needed after you install the package. So, if you answered yes, they will be uninstalled and will need to be installed again when you update the AUR package in question. But if you answered no, that’s okay too, as that will leave them installed for when you update the AUR package next time. So the choice comes down to either bloating up your system slightly or having to reinstall make dependencies every time you need them (slower update to the AUR package).