Well...standard reply. It's very hard to assess your situation without a diagram. Your verbal description is fairly good, but it's hard to sort out missing details and incorrect assumptions merely from a verbal description. But, things to consider:
- Make sure there's an EMF Absorption diode on that Relay.
- Make sure the Arduino output that is driving that Relay, is capable of driving that relay.
- Make you have your layout properly routed for delivery of higher currents. For instance, all Ground lines to the same point, and all Power lines to the same point. Sufficiently large gauge wire to handle the higher currents.
- Decoupling capacitors in strategic positions in your circuit, to supply local power, on demand, and prevent current spikes in the rest of the power lines that might induce voltage noise in the more sensitive electronics.
Also, I'm not sure what the statement:
A laser Pointer that is around 2.5 Vs
means. But that could just be my ignorance showing 
fodelement:
...does having the USB plugged into the Arduino while also having the batteries plugged in mean I am giving the circuit more power?
Probably not, but without a diagram, it's hard to say what is happening -- for instance, how do you have those two sources tied together? Also, have you tried it with just the USB connection?
fodelement:
What is the best way to determine the power needed for a project? Is it, to get the specs for everything and just add up the voltage? (I know very little about power needs and consumption, as you can tell with my 4 AA battery fail)
Again, hard to advise without a diagram. But, generally, you determine the power needs of each item, and add it up. But, since you are controlling the Pump with a Relay, not sure what power source you using to power the pump, and how you have that all arranged. The arrangement can be critical, in such a setup. So, a photo would also be nice.
fodelement:
...everything else is powered by 4 AA batteries.
If you are connecting these batteries to the Vin pin, the voltage regulator dropout will, likely, reduce that to a voltage too low for the Arduino to function properly -- especially if the relay is loading the batteries down enough to drop their voltage even lower than the nominal 6V -- also, as the batteries drain, their voltage is going to go below 6V, and the situation will get even worse. And, if you are connecting those batteries to the +5V pin, well, then, you are risking the destruction of your Arduino.