Recommended way to clone functionality to create a site in Drupal 8
If you want to just extract specific functionality, you need Features.

If you just want to clone an entire site, first you need to export the site config with drush. Then, you will need to wipe all UUIDs from config export files using a script, here is an example:

#!/bin/bash
FILES=/path/to/your-site/config/*
for f in $FILES
do
  echo "Processing $f file..."
  sed -i '' '/^uuid:/d' $f
done


From here, you can install a brand new Drupal 8 site, and then drop the config in and do a drush cmi to overwrite the entire config state to the one you exported.

I've used this method a few times to clone entire sites. You don't need to copy the database, in fact I would strongly advise against this.

If you wanted to make an install profile, you could do that too, and one route to doing that is to put your feature modules in a profile, include them as dependencies in the profile info file, and optionally add an installer script to configure the site a little further (default content?). But yeah, you will have to dive in a bit here.