1. I do not advise throwing it down the sink.

2. Put it in a capped, glass jar and reuse it. The dirt will sink to the bottom and the oil will remain dissolved in the liquid. Decant the liquid for the next cleaning session. You can wipe the bottom of the jar out with a rag/towel and throw it away, taking the dirt with it.

3. I like the coffee filter idea, too.

4. Clean solvent is not necessary, as it gets filthy as soon as it hits the chain.