Obviously this depends on how gear shifts you do . Recharging is needed surprisingly few, I guess every few months. I probably charge a bit early when I want ensure I won't run low, say before a holiday or a big important ride. Don't worry, there are indicator lights informing you of the current charge. Don't worry, never. The LBS needs to plug in their "relay" type unit that links your DI2 to a puter for diagnostics or customizations. (Not many home mechanics will have this bit of kit) They will up update firmware then. http://www.bikerumor.com/2013/10/23/how-to-update-shimano-di2-to-multishift-customize-button-function-change-shift-speed/http://e-tubeproject.shimano.com
Batteries will last about 3 to 5 years before having to replace them depending on how you care for them; but servo motors last about 2 to 5 years according to the RC world, and that should be one of your biggest concerns because once a servo fails you'll have to buy another derailleur.
And the reason most home mechanics won't have a diagnostic kit is because that's the whole idea from manufactures which they learned from auto manufacturers, and that is to get the buyer back into the shop to spend their money there instead of working on it ourselves at home.