How can I measure DC power with i2c?
To answer the parts of your question that deal with power rating for the current-sense resistor.  

It's good that you are paying attention to such things.  Yes, it's not uncommon for a current sense resistor to have a fairly small value and a fairly large power rating.  That's a norm.  

For an example, look at the development board for the LTC2946.  The manual contains a schematic.  The resistor in question is designated RSNS.  The manual also contains an abbreviated BoM (bill of materials).  RSNS is described as a 1.0W resistor in the BoM.  1.0W is comparable to the power rating which you have calculated for your application (don't forget to add safety margin, by the way).