Some ideas

An idea for a waste burner:

This would be for paper waste.  It is designed for catching embers so that they won't catch anything on fire. 

It is simple really.  Just use a terra cotta planter as the receptacle for the waste.  Build a small table like thing with a metal screen on top of it in order to catch the embers. 

Use it as follows:  fill up with waste and set it on fire.  Push the table into position, which will allow the waste to have air to burn, but catch the embers.  Simple idea, really.

This gave me an idea to use the same kind of set up to filter rainwater.  Instead of a wire mesh screen, use a cloth instead.  The cloth will stop some of the dirt and larger objects.  The terra cotta planter would be replaced by a water jug or something to hold the water.

In order to save time and money, just reuse the same device as for the burning of waste.  Place the cloth on top of the screen.