Multiple VBO fields on the same display ?

You need a custom action for sure.
Read the docs, you can pass the entire result row to your action execute method and do whatever you wish there.

But the available actions work, the thing is that as soon as I put more than one VBO field, only the actions of the first show up.
I need the ability to process (same kind of) actions on different entities in the row according the chosen field (only one at a time).
The workaround is to create one display per field to process

I'm afraid you'll need to implement such a functionality yourself then. I wouldn't recommend doing it on 7.x though, you're not going to get much support.

Thanks for the recommendation, but Drupal >D7 is way to difficult to handle for non-geeks...
We are using it as an efficient prototyping environment.