Greyscale Raster (tif) in ArcMap

I've used irfan view in the past to create grey scale tiffs, so you could try that. It will also allow you to batch up the conversion and best of all its free to use!

Your image is a three band composite that is rendered in color by default. If you use stretched, you will only show one of the three bands, so you could end up with the strange shades of grey that you are showing. For a background grey scale image, the best solution is to compute the INTENSITY of your color image.

This can be done in different software. With ArcGIS spatial analyst, you can add the three bands individually, then use the map algebra (raster calculator) to compute the average of your three bands ("im-band1" + "im-band2" + "im-band3")/3 . Principal component could also yield some nice results, but it is very "image dependent"

Since there are many issues adressed to georeference in posted answers, I'll try to explain the idea of georeferencing rasters.

Images are stored as raster data in which each cell in the image has a row and column number (in other words - pixel address). Then to tell GIS software how to translate row and column position into geography wise position there need to be information about georeferencing passed (transform parameters - translation, rotation, pixel size in geoprojected units).

Some image formats (like GeoTIFF) have this information stored in file header, others (like BMP, JPG, TIF) needs to be served with additional ACII file information - so called World file. World files are automatically loaded by GIS software if only their filenames suits images filenames (like when in the same directory are files image.tif and image.tfw). For further reading: See ESRI help page

Then every raster file can be processed in any graphic software (IrfanView, GIMP, Paint and so on) but you must be aware that any operation will cause file header to be flushed. So if you edit GeoTIFF it will loose it's georeferencing information.

To preserve this you should generate separate World file before graphic processing.

The easiest way to do that is to use Export Raster World File in ArcMap (manual reference).

If not using ESRI's software please read this GIS.SE post

Remember to save edits with same filename to link it with exported World file.

Hope it clears a bit.