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With the information I have I don't believe that the battery being installed six months ago would have anything to do with a problem now. The exception would be if a shop was looking at it now and somehow determined that the problem happened six months ago and was somehow covered up, etc.
If a battery is connected backward it can definitely cause fuses to blow or damage to any of the electrical components, but the damage is immediately. You can't connect a battery backward, connect it correctly and then drive the vehicle six months before something happens. If something is going to fail it will do it immediately, before you even realize you've connected it backward.