I have a new, HP Pavilion g6z laptop with Windows 7 Pro. My question is general in nature. Since I use my laptop usually at home, can I remove the battery and power it from AC only? Would doing so prolong the life of the battery?
Yes you can, but there is no benefit from doing so. Today's notebooks are powered by smart adapters which do not overcharge the battery, and unless you strictly adhere to maintaining the proper charge level of a battery to be kept in storage, you may do more harm than good.
What I do recommend is at least once a month, unplug the adapter from the wall and let the notebook run off the battery down to where you get the low battery warning, then plug the charger back in. In other words, fully discharge, then recharge the battery for best battery performance and duration.