If only one kidney is functioning at 13%, should one go on dialysis and if I did would the treatment prevent further failure?

Judgment is needed. Overall function is measured as "gfr" or glomerular function rate, + represents the amount coming from all of your kidneys (1 or 2 native kidneys, + any transplanted kidneys). The judgment to start dialysis may be clearcut (e.g., if too much fluid is retained or potassium is too high), or less urgent. Most pts with symptoms feel better after even 1 treatment, but it won't prevent further failure.
Not necessary. If you have a single kidney with 13% function or better called GFR of 13 ml/min, you do not need dialysis unless you have symptoms like lack of apetite or nausea.Better to investigate wheter you can get a kidney transplant or investigate ways of doing or preparing for home dialysis.
?Only 1 kidney works. You have fairkly severe kidney impairment if you only ahve one functioning kidney & that is at 13%. There should be little concern if you have anormal functioning kidney on the other side. No you should not go on dialysis, this is unlikely to prevent further kidney failure. You should be under care of a nephrologist, be on a low protein diet, plus other necessary medication, ie for hypertension.