when exactly do i activate a companion giving me additional Cards?
Do i activate them? I think not.
Am i allowed to save unused Actions and take them to the next round?
Well, in our last game we used all our Actions without any problems not even thinking about it. This question is only important if anyone is asking about it.
NASA Dawn approaching Ceres
You don't need to activate any cards to get the benefit on the bottom of the card.
You can't save actions for the next turn.
Even Cleverer Overtext
The Hellfish Bonanza!!!
Specifically, the "School Chum" cards that allow you to draw extra cards take affect in your planning phase. Basically, you just add your Chum's benefit to whatever you would have drawn from your planning space.
For example, if you have the +3 blue cards Chum, and you placed your planning marker on a space that draws 2 cards, you would draw 2 cards of your choice and 3 additional blue cards.