the + should be connected to power from the battery but i think chances are good that it died just because it says emgo on it
you may be able to get a warranty replacement but i think ultimately you'd be better off getting OEM coils or a higher quality replacement.
there should be a fuel strainer inside the tank, covering the intake tube of the petcock. if that's present, then no additional filter is needed, as long as you've cleaned the entire fuel system thoroughly. and that original setup is the best for flow, have a look at the parts diagram.
i've noticed this myself when i had an inline filter installed temporarily. especially after switching to reserve, it regularly disrupted the flow and starved the engine of fuel. since i get rid of it and went back to the original in-tank filter, it's all good. also make sure your fuel lines are the correct length and diamater so that their routing allows fuel to flow with minimal restriction, and helped by gravity.