The idea of sculping the iceberg to reduce drag is interesting... perhaps less like a sphere and more like a hull would be a bit more efficient. Though it might happen naturally in warmer waters as the iceberg is pushed North and the rougher edges melt away.
Also, the melting ice itself might reduce drag.
Would need to just go ahead and do it once with the ice berg as-is to practically baseline the efficiency.
Your guesses here are very good. Iceberg towing has been studied a lot (though if you look through the many reports about this online there is a curious tendency for people to think they are analyzing this for the very first time and approach it with a blank slate).
Yes, icebergs do naturally assume a hull-shape as they are being towed, and yes melting does reduce drag (if only because it keeps a clean smooth surface).
Shaping an iceberg with a little blasting is straightforward - ice is really easy to drill through to set blasting charges.
A lot of people posting thoughts on this seem to be looking for ways to save the water loss - neglecting the fact that the ice source is free, abundant, and constantly renewed, and thus the only cost associated with any melting is the towing cost incurred thus far for that fraction of ice that melts. As long as the loss rate is tolerable (fairly easy to estimate really) then there is no problem that needs to be "fixed' with more complicated schemes. Most of the suggestions to 'improve' the process drive up costs dramatically (cutting it up and putting it in a supertanker, wrapping it in plastic for the journey, etc.).
Once in place at Dubai the iceberg would be surrounded by a floating plastic containment curtain and seawater pumped out and replaced with fresh as it melts, forming a reservoir.