Merging Raster Datasets of Different Resolutions using ArcGIS Desktop?
Question 1
The attached script mosaics a list of rasters into a new raster dataset. Make sure to specify "MINIMUM" if you would like to maintain your 10m resolution raster datasets.
Question 2
Bilinear interpolation and cubic convolution are both good choices for resampling continuous data. Nearest neighbor is best for discrete raster datasets. Keep in mind that resampling a 30m resolution DEM to 10m will not improve the quality of the DEM, but rather will create more pixels that represents 30m resolution.
Question 3
The Mosaic to New Raster (Data Management) tool is your best choice.
You can see Mosaic to New Raster does a great job at merging overlapping rasters and color balancing.
import arcpy
from arcpy import env
# Set overwrite
arcpy.env.overwriteOutput = 1
# Set environment
env.workspace = r'C:\temp'
Dir = env.workspace
# Produce a list of raster datasets
rasters = arcpy.ListRasters()
list = ";".join(rasters)
# Raster to new mosaic
output = "new_dem"
arcpy.MosaicToNewRaster_management(list,Dir, output, "", "", "", 1, "MINIMUM")