Freedom in computing - is (A)GPL enough?

[ilias.k.cs at freemail.gr]

Hello and thank you for your efforts,

I'm a software developer from Greece. With the Snowden leaks, my worst suspicions seem to be true.Ever since then, I've been trying to replace all of "my" proprietary software with free software (and all of the services and formats I've been using with free equivalents).

It was very easy to commit to this decision as I know that with free software I can do everything I did before and in many cases better. 
However, its realization can be a little tricky sometimes, as for every software package (and format or service) I'm interested in, I've got to make certain that it is actually free. 

Being open-sourced or licensed under a permissive license, even under GPL, is ofcourse a good pointer but does not seem enough, as for example Linux itself contains blobs. 
Checking at the fsf directory for the package is something I always do, but if is not there, this doesn't mean it's not free.
And for formats, I mostly check FSF and Wikipedia.
As you know, services make the situation much more complex. For example, I'm interested in distance learning and MOOC services like http://www.complexityexplorer.org/ are a gigantic temptation for me. But I want to know what systems are being communicated when I make a request to such a service.
EdX is open sourced under AGPL, but is this enough for me to know?

In short, how can I know what a system I am using actually does, in a legal way, besides sticking to the systems I know for certain that are free? How do we deal with uncertainty?

Many thanks and sorry for the long post.

Ilias K.