qgis - Reprojecting a population raster from LAEA to lonlat

I have a population density raster from the EEA which is based on the CORINE land cover 2000 data.

http://www.eea.europa.eu/data-and-maps/data/population-density-disaggregated-with-corine-land-cover-2000-2

The population density is given in inhabitants/km^2, the resolution is 100mx100m.

My goal is:

1. 
   

   extract a country from the data by means of a shapefile from gadm.org

   
   


2. 
   

   convert it to a population COUNT raster

   
   



3. 
   

   reproject it from laea/GRS80 to longlat/wgs84

   
   


4. 
   

   aggregate/resample it to match climate data resolution (0.11°)

   
   

I do the first step with QGIS, I load the whole .tif, then select the shapefile as mask. Then I use the rastercalculator to divide by 100 to get the population count per cell.

First weird thing: R (using raster/rgdal packages) tells me that the minimum value is -1 (or -0.01) for the clipped (or clipped count) file, which is strange for a population raster.

The reprojection part doesn't work at all, as I understood, I'd use ngb for categorical data which I don't have. Bilinear resampling gives me a lot of negative values though.

The same problem occurs once the data is in the correct coordinate system, but not in the right resolution.

I first used the aggregate function in R to get the data close to the desired resolution, then used the resample function

Which is the correct reprojection method? How can I preserve the integrity of the population count?

Original data is in +proj=laea +lat_0=52 +lon_0=10 +x_0=4321000 +y_0=3210000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs

and should be transformed to +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0