Run a script in the same directory as the current script

Since $0 holds the full path of the script that is running, you can use dirname against it to get the path of the script:

#!/bin/bash

script_name=$0
script_full_path=$(dirname "$0")

echo "script_name: $script_name"
echo "full path: $script_full_path"

so if you for example store it in /tmp/a.sh then you will see an output like:

$ /tmp/a.sh
script_name: /tmp/a.sh
full path: /tmp

so

1. Knowing the current working directory is useless to me, because I don’t know how the user is executing the first script (could be with
   /usr/bin/script.sh, with ./script.sh, or it could be with
   ../Downloads/repo/scr/script.sh)

Using dirname "$0" will allow you to keep track of the original path.

2. The script script.sh will be changing to a different directory before calling helper.sh.

Again, since you have the path in $0 you can cd back to it.