Trying to understand Battery Chargers vol.2
Ok, so I've done some more research on the matter and apparently my quetions have been answered in older posts.

Custom solution 1

Custom solution 2

Custom solution 3

Complete IC solution

So, to answer my own questions,
1)The rest of the load should be located before the battery charger IC like in custom solution 3, in order to be considered a load.
2a) It is not about allowing more or less current, it is about the circuit topology which is completely wrong in my schematic.
2b) Well it can because, again, it is a different topology that allows that and in this topology the rest of the load is not simply placed after the battery without any intelligent control mechanism.