Regarding battery day: basically, Tesla will be able to make batteries that are cheaper, last longer, and are physically smaller for the same energy content compared to anything else on the market. The obvious application is of course cars, but there is a huge additional market for such batteries. Think for example laptops, mobile phones, smartwatches. Of these, it is in smartwatches that the battery size and capacity is by far the most important factor.
Which could explain the hints that Tesla is getting into the smartwatch business - its much better battery, coupled with its proven software skills and UI experience could mean that it could in fact threaten the apple smartwatch.
Tesla is not the kind of company that would sell JUST batteries - it wants the high margin profits of the final product
Thus it would not want to sell batteries if it can build the final product itself. So a Tesla watch seems reasonable indeed. Tesla laptops or tablets or smartphones do not seem realistic at this point - too much additional work required (although a Tesla smartphone could one day be competitive with not too much extra effort - perhaps after the successful introduction of the Tesla watch).