Error message 'source: not found' when running a script

/bin/sh is not bash. To execute your script with bash, write #!/bin/bash as the first line in your script.

The error source: not found is not dropped, because /etc/profile is not found. It's dropped, because source is not found. source is a Bash built-in function, and you don't execute the script with bash. So it's clear why it is not found. Change the #! line in the script, and it will work.

1. How can I be sure that the script is executed by Bash, even if #!/bin/sh is specified (apparently, it does not guarantee it)?

To be sure that a script written for sh shell (as in your case - see What is difference between #!/bin/sh and #!/bin/bash?) is executed by Bash, just run the following command:

bash script_name

Thus, you will not get that error anymore.

2. Why would it say that these two sources cannot be found when they are unmistakably there?

It doesn't say that those sourced files are not there. It says that the source command is not found. This is normal, because since you start your script with #!/bin/sh line, your script will run using sh and not bash as you may think. Why is it normal? Because source command is a Bash builtin, but not a sh builtin. To source a file in sh, you should use . (dot). Example:

. /etc/profile
. ~/.profile

Another way is to change the shebang line to #!/bin/bash as chaos said in his answer.

Some shells support . instead of source. So you can try something like this

. filename

instead of

source filename

Hope it works