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What year, model, and engine size of vehicle?
Does battery eventually die?
To me it sounds like your alternator is failing. I'd start by monitoring battery voltage during problem, if it is lower then 13v remove the alternator and have it bench tested at your local parts store. The alternator failing will cause low voltage nd the low voltage could cause your other problems. Let me know how it goes or if you have more questions. Thanks.
No problem, let me know how it turns out or if you run into problems. Thanks again and have a great day.