Understanding flow of current from diagram using AND gate
Don't think of the red lines and arrows as current flow - think of them as a low impedance path. The arrows point towards the destination object i.e. in the case above, the "a" or "b" lines being zero would "activate" either of the two parallel P channel MOSFETs that would then pass logic 1 through to the output stage: -



And, regarding the MOSFETs, these are the symbols: -



Picture from here.

Sure, the arrows are deceptive but, like you said in your own words: -


  it's HORRID


And if it's meant to indicate current flow, then it's horrid so, think of it as a low impedance path.