That may depend on other factors. Charging batteries get warm. They can get warmer if they're being charged at faster rates (quick charge vs slow charge). Also, if they're charging more, like now you charge at 10% vs before you were at 50%. Finally, batteries age, and as they do so they become less tolerant to charging, including a propensity to get warmer. This could just be a change in how you're using the device, charging it, or an effect of age.

I've had a couple games do that, even native ones. They were tested and launched expecting a default system, and as such didn't hit a race condition or other resource contention that they would at a faster speed. Happens more than you may think.

Using scripts or a QBW to launch them would probably be just as good as any other solution. I did that for TowerBloxx and it worked just fine. (At 500-900 it would get choppy, at 250-600 it was smooth... go figure...)

I haven't for about 6 months now, and my activity on them was low to start with. But in general I found it was more about how you were connected than what you had running. Running on 2G or wifi was fine; running on 3G drained. I also found that having bluetooth on in some areas (void of other devices) was fine, where in an office setting it was quite draining, even when not being accessed. (Apparently the bluetooth stuff wakes the CPU for most processing needs, which would cause far more battery use...)