Direct Injection of water to ...

Direct Injection of water to borewell

Yes you can directly inject the water from ROOF rain water harvesting system as the water is clean. And as you are also using the filter then there will not be any problem of any trash entering in the bore well. But the water can contain some bacteria which can affect groundwater quality, so make sure that the bore well is subjected to chlorination every time water gets injected into it. Also you need to be careful while injecting the water directly as some time it may  create air bubble in the pipelines.
In case if the filters are not working then store the water in some tank first and let the sediments and impurities settle at bottom and then inject them to bore well.
Now about your your second question, the recharge depends on the type of soil, type of aquifer of the region etc. So you have to check the site situation first. Even you have to check if the direct injection of water is permitted in your area. As I know some states do not permit the direct injection of water in bore well, then you have to sue the pit method.
If you want more details please write back at jamie.skolnik@gmail.com