First off, we prefer it if you used smaller pictures or thumbnails linked (or just links if thumbnails are unavailable) to the larger corresponding picture. Large pictures clutter up pages and screw up the formatting, making the whole page more difficult to read. Generally, pictures in a forum post should not be larger than 800x600, though 640x480 is safer. (personally I think width is the only concern as long as it's not a longcat picture or something)
I noticed there is no spring behind the trigger piece, which I believed to be common to almost every soaker that uses a pull valve. It looks like the trigger piece was cut and a burr of plastic removed that was used to hold the spring in place but if I'm wrong someone can confirm otherwise.
If you do need a trigger spring, they can be found in hardware stores. You'll have to look around and figure out what they look like (just over 1" long and fairly thin, with roughly 4mm between the spring's turns) This is unlikely to fix any real problems but may help slightly. For now, I'd say not to worry about it especially until someone else can confirm that the Monster X indeed has such a spring.
For the pumping problem, you are most likely correct. The valve is formally called a pressure relief valve, or PRV, and a common modification is to remove it to allow for higher pressures on the pressure chamber (PC) which is usually done by layering additional tubes over the bladder. (see modifications for more)
Removing the PRV should fix your problem, but be aware that there is no longer any safety to avoid over-pumping. Over-pumping will result in the bladder expanding too far and possibly damaging the reservoir if whoever is using the blaster presists in pumping even when the pump gets stiff. A small explosion could also occur. However, removing the PRV appears to be your only option since it's broken. A guide to removing the PRV can be found
here. Be sure you identify the valve correctly, which should be easy if you know how water guns work and where the check valves would go. (if not, read up
Next, it sounds like your trigger valve (pull valve) may be having problems. The most general fix to this is to wrap rubber bands to hold the valve closed or to put a spring behind it. Depending on the situation, one fix is likely to be easier than the other but both generally work effectively. (however, rubber bands may wear out more easily over time; keep this in mind) Opening the pull valve is somewhat rare and should only be done if it's not sealing. A guide for most pull valve issues can be found
here but it does not go too in-depth into fixing the common pull valve problem where the valve does not shut. Lubricating the pull valve may help it move better as well and prevent leaks and valves that don't close when the trigger is released.
Good luck with the repair and be sure you have a plan before doing something. Post back to confirm and clarify the problem assessments too; knowing the layout of a water gun well before undertaking mass repairs will be very helpful.
