Q: Starting vehicle after a few hours of being parked.

Usually happens early in the morning or when I get off of work. When the engine has been off for a few hours or more. I'll turn the key, I'll hear slight clicking coming from inside the dash/under the hood. The engine will turn over just fine and the clicking only lasts a few seconds. The speedometer and rpm gauges will slightly flicker and jump around a bit during the duration of The clicking. Sometimes the clicking will still be occurring even after the engine has already turned over. If I shut off vehicle and do it again right after. Most of the time it won't do it again. It will start as normal. The dash lights may go dim for a bit but that's all. Every now and then it will do it more than once. Most of the time only once. Vehicle still runs just fine. Except when in idle( at stop light or stuck in traffic ) idling rpms will dive below 500 rpms and vibrate the whole car when turning on ac. Do I have a failing battery, alternator, or starter?

My car has 41000 miles.
My car has an automatic transmission.