Why am I getting "An internal error occurred while preflighting your volume for APFS conversion"? I have a Mac Mini 2014. I just installed a second SSD drive Samsung Evo 500GB and would like to use as the primary drive for OS.

I formatted both drives with disk utility to OS Extended Journaled and clicked install Mojave but got this error. 

If I format the drive as APFS, the installation starts but after the restart, I get a blinking folder with a question mark. If I try to install from an external USB, instead of the folder with a question mark, I get booted into Recovery again instead of continuing the installation process.

Any ideas?
Try to install on the old disk first, to see whether there is a hardware issue with your new disk, for instance by copying a lot of files to it. You can also then install a second copy of your OS to the SSD and see where it fails.

Once both work, if you boot with ALT and press CTRL, it will save the ssd you are booting to as default.