Having the battery either in or out of your laptop will not harm your laptop in any way, so it's your choice. It will only affect the life of your battery.
http://batteryuniversity.com/learn/article/how_to_prolong_lithium_based_batteries discusses how to prolong the life of your battery.
http://batteryuniversity.com/learn/article/charging_lithium_ion_batteries is a good article discussing the charging of Li-ion batteries.
As you observed, having the battery installed in the laptop makes it feel more comfortable on your lap. It also offers uninterruptable power supply functionality should there be a power outage in your house. This can prevent loss of work {or effort you spent to reach a certain level in a game).
GPU temp is looking good. I recommend running HWINFO64 to monitor your CPU/GPU temperatures and fan speeds.
G74SX-A1 - stock hardware - BIOS 202 - 2nd Monitor VISIO VF551XVT