Nitrates and algea are related, although most algea cannot process nitrate, mitrate comes from ammonia, and ammonia is the principle source of food for algea. If your nitrate levels in you tank are rising rapidly, then there must be a good constant source of ammonia that the bacteria is processing. Ammonia may well be below detectable range, but it is there if you are getting rapid nitrate climbs. Most importantly what are your nitrate levels climbung too?, and what do they drop to after water changes?. It is unlikely that Nitrate is killing your fish as well. High nitrate levels will eventually lead to stress and disease, but aren't immediatly detrimental to fish or snails especially. Snails can live in some pretty nasty water for long periods of time. What type of algea do you have?, this may help us help you as well. There are ways to get things under control, but there is an underlying cause to all of this that will have to be addressed. We need some more information to be helpfull such as:
tank parrameters
Age of tank
stocking level
supplements if any
maintenance routine
Feeding routine and amounts.
As far as an immediate start, start with big daily water changes for two or three days, then do a 4-5 day blackout (no light at all, cover the tank glass) Do not feed during the blackout, but you may want to do a large water change in the middle of the blackout to remove dead algea. Then follow the blackout with 2 or 3 more big water changes, and see where you are at. This should put your tank back in excellent shape, and give you a fresh start. then you need to figure out a better feeding lighting and maintenance schedule.
Dave