Hi Goral,
I'm on a train... just starting Qgis!
1. OK in Qgis you can use:
- 'Raster'
- 'Conversion'
- 'Rasterize (Vector to Raster)...'
You may need to take a backup copy of your shp file and edit the attribute table first. I did when I did a similar thing for 'roads'.
It can be slow but it should work.
2. Are you trying to make a file that shows distance to the nearest river at any point? I did something like that and I'm trying to remember how I did it! I was using my big machine rather than my laptop and I may have loaded a 'heat map' plugin to run the analysis. I will look that up when I am back at my desk in about 10hours time!
Cheers
Steve
PhD University of Wales