Can I determine my vision from my corrective lens prescription?

Roughly. There is a rough correlation between the prescription and the vision chart-- for each line on the vision chart, there is approximately 0.25 d change in the prescription. So you can estimate your vision based on this formula.
Not really. The numbers in a prescription only define far or nearsightedness and astigmatism. Rough estimates can be extrapolated from the prescription but can be affected by retinal, corneal or lens disease. The best way to see what the "best corrected" vision with glasses is to use an eye chart.