I'm able to select them just fine, but I have a different OS and Java version than you.
Try the latest Java 8 Hotspot from AdoptOpenJDK.
Note: You may need to uninstall Oracle Java for your computer to properly choose the AdoptOpenJDK version.
Please provide the installer log
It will be in the same place as the installer and either have the same name but with ".log" on the end, or be called installer.log
_mapped_ deps aren't stored anywhere because they would be against the EULA, so ForgeGradle generates them on demand.
Show the full log, this usually means something went wrong earlier in the process.
Some zip managers like to take control of the .jar file extension away from Java.
Make sure you have Java installed and try running Jarfix once, then try the installer again.
A) I hate "I'm not releasing it" as a reason to do things the wrong way or do things you're not supposed to
B) "Other people do it" is not a valid reason to do something