I leave my water pan inside my MES but it's empty and foiled over. Someone here advised me to leave it in since that was part of the smoker design. I don't know if it needs to be but the benefit of leaving it in and foiled over is that it also catches grease drippings which means less drippings actually make it to the grease drip pan below.
There's supposed to already be a hot spot in the right rear of the MES so I don't know if removing the water pan would allow the heat to be better distributed but I like to leave it in just for the grease drippings thing. I've found no difference in the moistness of the meat and smoke absorption with our without water. If you're going to add water, I'd say a cup should be fine. I used to fill mine up and that produced way too much steam for the interior size of the smoker.
I own the Maverick ET-733 and observe temp differences between it and the MES temp display all the time. Since I've been told there are heat variances inside the MES 30 Gen 1 (which is what I own) I'm going to play around more with placement of the probes in the smoker to see where I get the most accurate readings, both for Barbecue and for Food.
The MES 30 temp display will show temp swings, or at least mine does. I have the ET-733 set to sound an alarm when the temp swings past my minimum and maximum settings. If that happens I increase or decrease the temp accordingly. If it swings up to 15-20 degrees either way without going outside of my parameters I leave it alone since it will average out to my set point anyway.