On the first example you simply have 2 packages that are in conflict with each other and must remove one of them.
On the second you need to add the gpg key for the author (if you trust him) and that allows you to build the pkg:
gpg --recv-keys CFDF148828C642A7
All those AUR helpers do about the same thing, the issues that relate to security that ARCH people talk vaguely to condemn one and promote another relate to the fact that root should not be building packages in Arch, only a user should (there are good reasons for this .... for one a user can read libraries but can not change them, when you are executing code to compile a package you can't be reading the entire code to verify that nothing modifies your libraries) and that user can not "install" a package without root priviledges.
You have several branches of an aur helper.
1 Search for the package (PKGBUILD) file that you need.
2 Download the PKGBUILD, which is a recipe for cloning the source
3 Downloading the source git clone https;//......git.../pkgname-pkgversion
4 Building the package to become pacman compatible (prescribed by PKGBUILD) "makepkg"
5 Use pacman -U to install the package that was built.
makepkg is part of pacman, it is what builds pacman packages.
So it doesn't matter what tools you use, the outcome is the same. If you believe that yay builds packages differently than yaourt or cower or pacopts you are a fool that has fallen for Arch propaganda, as far as I am concerned.
yaourt (last version from a few months ago) as a package was 120K
package-query 1.11 is 28K
yay is 2,2M
cower is 27K
pacopts is 8.9K (which has other functionality internal to Obarun )
pamac is about 525K probably 700K + together with its gui and appindicator
So yay is way too big for the little it does.
Arch was meant to be a KIS/KISS distribution, ever since the systemd adoption it has been deviating more and more from that commitment.