This one seems to have slipped by under the radar. I'll advance my interpretations of how the Exo-Loader works - subject to correction of course
1. If you own a second Cell, can you immediately activate that? (I only ask this obvious question because the rulebook says you cannot use cards in your Inventory while inside the Loader)
I'd say yes, you can immediately activate any Power Cells in your inventory while inside the Exo-Loader.
2. If somebody else owns a Cell, can they trade it with your while your in the Loader? The rules forbid trading while in the Loader, but does this apply to Power Cells to? If not, is there any way for another person to "power up" your Loader if they have a Power Cell and you don't?
Or do you have to exit the Loader, trade for the Power Cell, then get back in it again?
I'd say, they can add a Power Cell to your Inventory but they can't take an Item from you in return. The Power Cell added can exceed your Inventory Limit so long as you are in the Loader.
3. If you leave the Loader while it is still "charged", what happens to the half-used Power Cell? Does it stay 'inside' the Loader so someone else can climb in? Or are you forced to take it with you?
It's simpler to say the Power Cell just gets discarded. That's a very inefficient machine, but presumably it's taken a battering and isn't working to full spec.
4. If you exit a still-charged Loader, how many actions do you have left? It takes an action to leave, but you had 4 actions while you were in the Loader: are you left with 2 or 3? What if you take 2 actions with the Loader, then exit the Loader: do you still have an action left?
The simplest rule is to say that you keep any unused actions: so if you start the turn in the Loader you have 4 actions; if you use the first to leave the Loader, you still have 3 left.
(The alternatives seems to be to say that leaving the Loader counts as two actions or that leaving the Loader ends your turn - both unattractive or inelegant).
5. If you enter a still-charged Loader (assuming that Loaders hold their charge - see 3.), does that still end your turn? If not, how many actions do you have left?
I'm going to rule there's no such thing as a 'half-charged' Loader, so entering any Loader ends your turn.