The low pressure pump (Google "Mity Vac" for an example of a low pressure pump) is just for testing the check valve, you apply a certain amount of pressure (I think 6PSI or less) to make sure that the oil check valve is opening and closing as it should. The check valve is mounted in the intake manifold, it is the port through which the oil is put into the cylinder after it comes out of the pump.
As far as adjusting the chain, just loosen the two bolts that hold the axle carrier in place at the end of the swingarm, then turn the axle using the large hex shaped part of the carrier. The carrier is cam shaped. so rotating it within the swingarm mount will tighten or slacken the chain. Be careful not to run your chain too tight, you can risk shearing a drive gear, or worse, cracking the case after it is hit by a broken chain. Once the chain is properly adjusted, tighten the bolts to hold the axle carrier to the swingarm, the torque spec for the nut on these two bolts is 30 ft/lbs. If you have an optional trailer hitch installed, the torque spec is 40 ft/lbs.
If you ever ride hard or have the quad off the ground on small jumps, you may want to consider an aftermarket chain tensioner to avoid running your chain too loose, but also avoid breaking the chain with it too tight. Scroll to the very bottom of the page linked below to see what I mean by "chain tensioner."
Also, if the chain is making noise, check to make sure all of the links move freely, if they do not move easily and freely, remove the chain, thoroughly clean it, then soak it overnight in oil. If they still do not move freely, replace the chain or risk damaging your case.
As always, Good luck!