My specialty. I have more data in my spreadsheet than I care to admit. I gathered all this when designing my own power system for some RC cars. To answer your question:

1. Your getting slightly higher RPM with the smaller battery and larger KV motor combo from your example. RPM is calculated as KV x voltage. Using our example.
2000kv x 22.2v = 44,400RPM
vs
4000kv x 11.2v = 44,800RPM

2. The stress level on the battery has to do with the amps. The more amps your battery can tolerate over the motor's rating, the less stress it will be. Amperage of the battery is calculated using Mah and the C rating. A higher Mah battery will need a lower C rating to achieve the same amperage as a lower Mah battery with higher C rating.
Mah x 0.001 x C rating = amps it can handle. You didn't provide Mah nor C rating of your battery comparison so I can't say exactly how this applies to your example. A higher C rated battery generally costs more, so you may want to keep that in mind. A larger Mah rated battery will generally be physically larger in size so that's something to consider as well. 6S lipo is a fairly large battery. Consider safety when charging. Also the larger the battery gets, the less efficient it becomes. The performance of the battery needs to be at least as much as the drawback of the added weight.

3. People think that a lower KV motor has more torque, but that's only true if the voltage is the same. In your case, your voltage is increased with a lower KV motor.