Mrkai, I would go to your local Suzuki dealer for a battery if you have one available. I had battery issues with the standard lead/acid batteries that didn't last more than 6 months brand new and I am a daily rider, so long down times weren't the issue. After the second battery, I upgraded to a lithium ion battery. It is pricey (105.00 US) but has lasted two years now and still going. It has a lot more cranking power and a fraction of the weight.
I can't help you on the rest of your electrical problems. You might want to connect with Alantf on this forum as he is very smart with those kinds of issues (there are others as well that will come on and help you). Good luck.
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