I've created a tutorial to address all the many questions that are asked in these forums, about various ways to create transparency or transparent areas in an image, using Inkscape. Extremely briefly, the following are keys to the 2 (in my opinion) most often asked:
- To export to PNG with a transparent background, please use File menu > Export Bitmap, and NOT File menu > Save As > Cairo PNG. Please read the tutorial for details.
- Inkscape cannot crop an image. The nearest equivalent command is called Clipping. Please read the tutorial for details.
I hope this will help you find answers on your own. But please feel free to ask for further assistance, by posting a reply here.
Also please feel free to let me know if you find errors in content or typing.