Regarding the battery, BMW has never been good on their selection of bike batteries (Exide). Mine began to slow crank at 6 months, especially when warmed up (?). I could have gotten another BMW battery from the dealer for free, but why mess with that when the Odyssey PC690MJ lasts so much longer and doesn't exhibit the hesitation and slow crank that the BMW branded ones do. My Odyssey on the RT ran until I sold it (7 years). The K is showing signs of slow cranks and hesitations now at 4 years (they warranty free replacements for 2 years which is pretty good for a bike battery).
On my last look, the BWM stock is around $179 for Max BMW. The Odyssey can still be found for $119 online or about $163 retail. Far better battery for the money over the BMW one. The military spe'd metal jacket allows it to be used in a higher temp environment by 50 degrees which is beneficial to those in the southwest deserts. You could also go to a TekBattery (lith-ion) and save weight, but they cost over $1,000 (ouch!).
Noise on start up is usually the cam chain and pressuring up the follower plunger. Not much you can do about it. Hopefully, it is not the other issue is when the gear begins to come off the end of the cam and the cam mechanism falls apart due to a broken flange that the gear bolts onto (crappy weak design, imho).
Stalling is something the K1200-K1300's are famous for. That software update seems to be the fix, although hanging the high idle and then dropping it is a pretty sloppy way of them doing it. I used to love the engine braking due to the high compression, but that seems to have left the planet after they tinkered with that - even on the 1200.
I'd say ride it 'till it blows chunks.