Yes it is the battery + terminal all the positive leads are red and all the negative leads are black all the black leads are tied together through out the car and the
It is conventional to put that sort of information in the schematic with the way it is drawn. That is one connection to the battery with all the other wires going to that point. That way you can see how it is wired.
That schematic is, unfortunately, of little use in seeing how you have wired your system. Imagine all you had was that schematic how would you wire it up. You can't.
For example all I see for the fog lights and so on is a block with some wires going to the arduino. There is no indication about how this is wired, where it gets its power from and how the arduino signals are connected to what to control these lights.
Basically there can be three types of things wrong with your setup:-
1) You have not wired it up as the schematic
2) The schematic is wrong
3) Not enough power capacity or decoupling
However without a schematic that shows where the wires go you just can't tell what is wrong.