A VO2 test essentially tests your heart and lung capacity. The lung surrounds the [mediastinum](https://en.m.wikipedia.org/wiki/Mediastinum) and the heart and stomach are the two main organs lying within it.

Therefore, as VO2 tests make your heart and lung (to be more precise: the diaphragm) work at peak power and their volume changes are at their maximum, there is immense pressure going on in this region. A full stomach, therefore, means that they cannot work at their full potential.

Another problem is that this pressure at high-intensity exercise leads to [gastric emptying delay, which is a main cause for exercise-induced nausea](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4027831/).

Long story short, if you want to see your full potential and don't like throwing up, your stomach should be relatively empty for the test.

As of caffeine, it's like @JohnP said: it elevates your base heart rate [and is (or rather because it is) a vasodilator](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3003984/). Therefore, it influences test results.