"But if the salt is trapped in the filter and water flows through it wont it cary the salt with it or is the filter so small that this will not happen."
It seems you slightly misunderstand how reverse osmosis for pure water works. Most of the water passes straight through the center directly to WASTE. This is the path of least resistance. The system works because you RESTRICT the waste line, which creates enough backpressure so that some of the water passes THROUGH the membrane. Nothing but water will make it through. Everything else gets flushed out the waste, which is the easiest path through the membrane.
Re: reusing saltwater...
you could in theory process your old saltwater, but it would be a bad idea IMO. The TDS content of the water is what determines how well the RO works. I'd be willing to bet that saltwater will exhaust an RO membrane much faster than tap water.
everything below this line is more speculation than anything since I cant recall the facts entirely.....
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I have read somewhere that DeIonization does NOT remove salt from water, and that it could be used to filter saltwater. I am not sure what the benefits of doing that would be though, and it seems expensive/wasteful (but I am lacking information). If anybody has information on this I'd be interested in hearing it.