You certainly don't NEED to keep it attached to AC power when it is shut down, but it will not harm the battery if it is. I'm guessing you are now charging to 100% and then discharging to a low percentage, and then repeating the procedure, yes?
yes. thats harming the battery?
Yes, it is unnecessarily increasing your cycles count. You already have over a year's worth of charge cycles on your battery in 2 months.
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