For the first, get something dense (so you don't have to fuss with corrections for the specific gravity) that weighs about 15 pounds (I'm assuming you have a typical kayaker's vest) and attach to the vest. The weighted PFD should just barely float. If it doesn't, you've lost buoyancy. By varying the weight (you can use a mesh bag filled with lead shot and vary the amount of shot, for instance), you can figure out how much buoyancy you've lost.

Look at the vest. If it is faded, with the straps and fabric starting to fray, then you have a lot of UV damage. Tug at the faded parts. If they start tearing easily, or the seams let go easily (the thread is usually synthetic and also subject to UV degradation) it's definitely time to replace it.

These two tests cover the two most common ways the vests degrade. One is the slow decomposition of the foam (which is invisible to you, being encased in fabric) causing loss of buoyancy, and the other is ripping/tearing and thus releasing the foam to float away (whilst you sink) during a "carnage moment."