Measuring distance between centroids R - r

Question

I want to create a matrix of the distance (in metres) between the centroids of every country in the world. Country names or country IDs should be included in the matrix.
The matrix is based on a shapefile of the world downloaded here: http://gadm.org/version2
Here is some rough info on the shapefile I'm using (I'm using shapefile#data$UN as my ID):
> str(shapefile#data)
'data.frame': 174 obs. of 11 variables:
$ FIPS : Factor w/ 243 levels "AA","AC","AE",..: 5 6 7 8 10 12 13
$ ISO2 : Factor w/ 246 levels "AD","AE","AF",..: 61 17 6 7 9 11 14
$ ISO3 : Factor w/ 246 levels "ABW","AFG","AGO",..: 64 18 6 11 3 10
$ UN : int 12 31 8 51 24 32 36 48 50 84 ...
$ NAME : Factor w/ 246 levels "Afghanistan",..: 3 15 2 11 6 10 13
$ AREA : int 238174 8260 2740 2820 124670 273669 768230 71 13017
$ POP2005 : int 32854159 8352021 3153731 3017661 16095214 38747148
$ REGION : int 2 142 150 142 2 19 9 142 142 19 ...
$ SUBREGION: int 15 145 39 145 17 5 53 145 34 13 ...
$ LON : num 2.63 47.4 20.07 44.56 17.54 ...
$ LAT : num 28.2 40.4 41.1 40.5 -12.3 ...
I tried this:
library(rgeos)
shapefile <- readOGR("./Map/Shapefiles/World/World Map", layer = "TM_WORLD_BORDERS-0.3") # Read in world shapefile
row.names(shapefile) <- as.character(shapefile#data$UN)
centroids <- gCentroid(shapefile, byid = TRUE, id = as.character(shapefile#data$UN)) # create centroids
dist_matrix <- as.data.frame(geosphere::distm(centroids))
The result looks something like this:
V1 V2 V3 V4
1 0.0 4296620.6 2145659.7 4077948.2
2 4296620.6 0.0 2309537.4 219442.4
3 2145659.7 2309537.4 0.0 2094277.3
4 4077948.2 219442.4 2094277.3 0.0
1) Instead of the first column (1,2,3,4) and row (V1, V2, V3, V4) I would like to have country IDs (shapefile#data$UN) or names (shapefile#data#NAME). How does that work?
2) I'm not sure of the value that is returned. Is it metres, kilometres, etc?
3) Is geosphere::distm preferable to geosphere:distGeo in this instance?

Answer 1

1.
This should work to add the column and row names to your matrix. Just as you had done when adding the row names to shapefile
crnames<-as.character(shapefile#data$UN)
colnames(dist_matrix)<- crnames
rownames(dist_matrix)<- crnames
2.
The default distance function in distm is distHaversine, which takes a radius( of the earth) variable in m. So I assume the output is in m.
3.
Look at the documentation for distGeo and distHaversine and decide the level of accuracy you want in your results. To look at the docs in R itself just enter ?distGeo.
edit: answer to q1 may be wrong since the matrix data may be aggregated, looking at alternatives