the greater the cross sectional area of a trace the greater the current capacity (less voltage drop) and to an extent the greater the cooling capacity (more surface area)
in this case they are using the solder as a cheap way to increase the cross sectional area, and the ripples have the added bonus of increasing the surface area for the same trace width,
As for the star shaped mounting, i'm pretty sure your talking about thermal reliefs, without them it is near impossible to get enough heat into a joint to cleanly relfow, essentially it acts like a thermal resistance, reducing how much of the heat from your iron goes into heating up a power plane vs heating up the joint,
And for the original OP, if your using very cheap PCB manufacturers, your Gerber's can be edited without notice so your solder mask may not follow the exact shape you had specified, (may be thicker or thinner, or removed on points of fine detail) so you cant even rely on it as a physical separator between 2 close pads,