Paul__B:
And eight LEDs in total. All single colour? Do the ones around the button have any special function? OK, I mis-read your original description.
8 LEDs total. They're all dual colour: red and green! 
The ones around the buttons have a special function but not one that I'm interested in at the moment. They always glow together as a pair. When you select a blind through the select button, the glow green when the paired blind is available and red if it's not (as in "in range", "we can talk"). When you push an action button (up/down/stop), they glow red to acknowledge your input then green if the blind replied back (it's bidirectionnal so you can tell if the blind really got the order).
The one to the right tells you the status the remote is in (programming or just standard mode).
Finally the 5 blind LEDs always glow green even though they're dual colour.
Paul__B:
matmat:
I'm not sure how to answer your questions regarding the way buttons and LEDs are connected. I mean how do I know in which direction I'm supposed to measure that?
Well, you trace the PCB tracks. For a start, it looks as if the LEDs all return to the positive rail. You can double check with a meter.
Well if I measure between the + from the battery pack and what seems to be the anode (the left side of the LED above the elero logo), I mesure 0 Ohm. So that's connected. And looking at the traces the cathodes go to the atmel chip (if that makes any sense).
Paul__B:
OK, so they are running off 3V, of course they are obviously red. 
2V when I measure and red and green. 
matmat:
So to sense them, you need PNP transistors with emitter to positive, and base to the other side of the LED through a 47k resistor. The collector will pull up to 3V (not 5V) when a LED is on. If the buttons go to ground, then NPN transistors can be used to spoof them. Clearly this unit has an automatic "sleep" mode (all LEDs off) if you have not used it for a certain time.
Ok the PNP thing is doable and the NPN as well (I even understand haha). Yes, the remote goes to sleep after a couple of seconds.
matmat:
Note that your Arduino will be operating at 5V (though you could I suppose use a 3V 8 MHz Pro Mini and interface it directly to the LEDs and buttons without the transistors - just the resistors for the LEDs) so you need to use a common ground (negative) and you can probably power the remote from whatever supply you are using (not batteries) with a 3V regulator (LM317). Another alternative is to use a 74HCT chip such as a 74HCT14 as a level converter for sensing the LEDs.
Mmmm now you're making me think. Less soldering would be easier I guess. I'll do some reading to understand what the 74HCT does.
matmat:
Yes, but probably nicer to monitor all five. A 74HCT14 would be easy, one chip and a resistor array..
Meh, five is overkill really as there's no other combination than only one on or all of them. Plus given I don't know yet what your 74HCT14 does...